Post on 27-Oct-2015
INDIAN MATHEMATICS RELATED TO
ARCHITECTURE
AND OTHER AREAS WITH SPECIAL REFERENCE TO KERALA
Thesis Submitted to the
COCHIN UNIVERSITY OF SCIENCE AND TECHNOLOGY
for the degree of
DOCTOR OF PHILOSOPHY
Under the Faculty of Science
By
P.RAMAKRISHNAN
DEPARTMENT OF MATHEMATICS
COCHIN UNIVERSITY OF SCIENCE AND TECHNOLOGY
COCHIN - 682 022, KERALA, INDIA.
SEPTEMBER 1998
CERTIFICATE
Certified that the thesis entitled -INDIAN
MATHEMATICS RELATED TO ARCHITECTURE AND OTHER AREAS WITH
SPECIAL REFERENCE TO KERALA- is a bonafide record of work
done by Sri. P. Ramakrishnan under my gu idance in the
Department of Mathematics, Cochin University of Science
and Technology, and that no part of it has been included
anywhere previously for the award of any degree.
Kochi - 682 022 September 25, 1998.
Cochin
Dr. T. Thrivikraman Supervising Guide
Professor & Head of the Department of Mathematics
University of Science & Technology
DECLARATION
This thesis contains no material which has been
accepted for the award of any Degree or Diploma in any
University and to the best of my knowledge and belief,
it contains no material previously published by any other
person, except where due references are made in the text
of the thesis.
Kochi - 682 022 September 25, 1998. P. RAMAKRISBNAN
ACKNOWLEDGEMENT
I am most grateful and deeply indebted to
Prof. T. Thrivikraman, Head of the Department of
Mathematics, Cochin Universi ty of Science and Technology,
for his patient supervision and valuable guidance
throughout my research. Timely suggestions and
encouragement of Prof. A. Krishnamoorthy, Department of
Mathematics, are greatly acknowledged wi th heartfelt
gratitude
I also place on record my thanks to my colleagues
in Cochin University and in the Cochin College,
Kochi 2, for their cooperation in carrying out my
research.
Finally, I wish to thank Mrs. Kochuthresia for
her good typing.
Kochi - 682 022 September 25, 1998. P. Ra.akrishnan
Chapter I
1.1. 1. 2. 1. 3. 1.4. 1.5. 1.6.1.
1.6.2. 1. 7. 1. 8. 1.9.1. 1.9.2. 1.10.!. 1.10.2.
1.ll. 1.12.1. 1.12.2. 1.13. 1.14.
Chapter 11
2.1. 2.2. 2.3.
2.4. 2.5. 2.6.I. 2.6.2. 2.6.3. 2.7. 2.8. 2.9. 2.10. 2.11. 2.12.
CONTENTS
INTRODUCTION
RESIDENTIAL ARCHITECTURE
Int roduct i on Selection of Site Solar Path and Shadow Method Formation of the Square Ma~9ala Location of a domestic building Determination of Grhav~dika using Grid system Vithi Systems The Concept of Marma The Concept of V~stupuru~a Units of Measurements Units in Manu~yalayacandrika The Concept of YOni Modular Coordination in Traditional Architecture Method of finding Perimeter and length Proportions in Traditional Architecture Gunam~a Method Types of Salas Vertical Elements of the building
~BMPLB ARCHITBCTURB
Historical Background Selection of Site for a temple Geometrical Method of Determining Cardinal Directions Classification of temples Alpaprasada Garbhagrha The Thickness of the Walls The Disposition of Garbhagrha Vertical Components of a Prasada Vertical Proportions Disposition of the doors Pa1\caprakaras N~tyamary9apam Talamana
Pages
(1-9)
(10-32)
10 11 13 14 15
15
17 18 19 20 21 22
25
26 27 28 29 31
(33-46)
33 34
35
36 37 38 38 39 39 43 43 44 45 46
Chapter III
3.l. 3.2.
3.3.
3.4.
3.5.
3.6.
Chapter IV
4.l. 4.2. 4.3. 4.4. 4.5. 4.6.
4.7.
Chapter Y
5.1. 5.2. 5.3. 5.4.
5.5.
5.6.
5.7.
5.8.!.
5.8.2.
5.8.3.
THE CONCEPT OF • -VARIOUS APPROXIMATIONS
Introduction Value of ~ in the Construction of Vrttapr~sada
Value of ~ implied in the construction of Gajapr~tha Shape Value of ~ in the construction of a circle with perimeter equal to that of a Square Approximation to ~ in 'Thaccusastram Bhasa' App~oximation to ~ in finding the Radius of a Circle
THE GOLDEN RATIO IN TRADITIONAL ARCHITECTURE
Introduction The Concept 'Golden Ratio' Golden Rectangle and its property Golden Rectangles and Fibonacci Numbers Golden Ratio and Arddh~dhika Golden Ratio and Natyama~9apam (Kuthampalam) Construction of Bimba (idol) and Golden Ratio
TRAlRASIKA (THB RULE OF THREE) IR ~RADI~IORAL ARCHITBCTURE
Introduction Definition of Traira~ika Vyasta - Trairasika Method of finding the inclination of the Collarpin on an inclined rafter Determination of heights of the roof for different pitches Some other proportions of height and width Determination of the length of the side of an Octagon Determination of length of Rafters using Traira~ika 8th Postulate (Ettam Prama~am) and length of rafters 4th Postulate (Nalam Prama~am)
(47-58)
47
48
50
53
55
57
(59-71)
59 60 61 64 66
66
69
(72-92)
72 73 75
76
80
83
84
86
87
89
Chapter VI
6.1. 6.2.I. 6.2.2. 6.3.
6.4.l. 6.4.2.
6.s.I. 6.5.2.
6.5.3.
6.6.I. 6.6.2.
6.7.
6.8.
6.9.
6.10.
6.11.
6.12.
6.13.
6.14.
GEOMETRICAL CONSTRUCTION AND RELATED MATHEMATICAL CONCEPTS
Introduction Square Construction of a Square Construction of a Rectangle whose perimeter equal to that of a square Circle Construction of a circle whose perimeter is equal to (approximately) that of a given square Gajapr~tha and Vrttayata Method of Construction of Drrghav~tta (Elongated Circle) Determination of the perimeter of the DirghavFtta Triangle Construction of a Triangle whose perimeter is equal to that of a given square Construction of a hexagon whose perimeter is equal to that of a given square Construction of an Octagon whose perimeter is approximately equal to a given square The method of inscribing an Octagon (Et~u~attam) in a given squar~ Method of construction of 'Srlcakra' (or Sr"iyantra) To find the length of the Diagonal of a square without using Pythagoras theorem Construction of Lamba and Vitana (vertical and horizontal direction) Geometrical method of finding the length of rafters Geometric method o£ determining the width of a rafter
APPENDIX
ENGLISH TRANSLATION OF MANUSYALAYACANDRIKA
SANSKRIT TEXT
BIBLIOGRAPHY
GLOSSARY
(93-135)
93 94 95
96 98
98
102 103
106
108
109
112
114
118
120
124
126
129
132
(136-229)
(230-272)
(273-284)
(285-295)
INTRODUCTION
Indian Mathematics in its broad sense is as old as
at least Indus Valley Civilization which is also true in the
case of Indian Architecture (V~stuvidya). The earliest texts
on Indian Mathematics are the Sulba (or Sulva) Sutras (800-
500 B.C.) which are compilations of mathematical principles
that have developed in India during ancient times.
Several geometrical principles are either explicitly
mentioned or implied in the
platforms, sacrificial halls and
( 11) measuring rod and thread or rope
construction of altars,
other things with a
(raj ju) . Since rope was
used for measuring length and breadth, in course of time,
geometry was called Rajju s8stra in the early period of
. (17) Indian Mathematics (gaoita) . The dev elopmen t of geomet ry
_ay just as well have been stimulated by the practical needs
of construction and surveying and this explains the relation
between geometry or mathematics and architecture in ancient
India.
The period extend ing from the 5th century A. D. to l7 th
century was one of general prosperity for scientific
development in India. ~ryabhata I (b. A.D.476) was the first
among the top ranking mathematicians of ancient India, as
he had not only introduced many new theories and formulae
but also anticipated discoveries of modern times. He has
2
also laid the foundation of different branches of
mathematics. Var~hamihira (A.D.SOS), Brahmagupta (A.D.628),
Sridhara (A.D.7S0), Mahavlra, Sripati and Bhaskara (b.
A. D .1114) are some of the scholars of th is per iod who made
notable contributions to the twin disciplines of Mathematics
and Astronomy.
It was an evolutionary period of Indian architecture
and the historical evolution of architectural theory is
traceable mainly from manuscripts and published treatises,
from critical essays and commentaries, and from the surviving
buildings of every epoch. According to P.K. ~carya there
are about 300 texts on architecture in India in different
languages. Varahamihira's Brhatsamhita of century A.D.
gives an authoritative treatment on building temples and
houses, in two separate chapters. Is~nagurudevapaddhati,
" 'Klmik8gama, Samaranga~asutradhara, Mayamata, and M3.nasdra
are some of the compilations on Indian architecture
(Vastuviaya). All these works are comprehensive and masterly
compilations in highly technical Sanskrit. Even though,
Mayamata and Manas3.ra were treated as reference texts all
over India, some variations in details were adopted in
regional texts because of the geographical and climatic
differences of different regions.
In Kerala the Mah~dayapuram(2) period (9 th century
A.D. th to 12 century) marked an all pervasive transformation
3
in the pol it i cal, social and cuI tu ral fields and the earliest
known structural temples in Kerala rose in the first quarter
of the 9 th centu ry (A. D. 823) . Even t hough the temples were
constructed according to v:"!!!"stu principles that was prevalent
in India, a unique style of architecture was evolved in
Kerala and attained perfection during the late medieval and
early modern periods
Stella Kramrisch(38) calls
century A.D.
them purely
to century) .
Kerala shapes with
their high sloping roofs and angular silhouet tes, in temples,
mosques, palaces and churches. There had been an effusion
of mathematical, astronomical and architectural
investigations during this period. As a result of this, a
large number of treatises were formulated in these
disciplines. We concentrate our investigations on Indian
mathematics related to architecture to this period only, with
special reference to Kerala.
V@ovaroha and other works of Sa~gamagrama Madhava
(GOlavid) (1340-1425), DrggaJ;li ta of Parame~wara (1360-1455),
Tantrasaugraha of Nilakar;t tha S~may~j i (1443-1545), Yukt ibhaliSa
or GaoitanyayasaQgraha of Jy~~tadeva (appr.1500-1610) etc,
are some of the contributions of mathematicians and
astronomers of Kerala during this period.
(Rationale in Malayalam language) which is composed in
Malayalam language deals with several branches under
mathematics and astronomy and even ci tes examples from
traditional architecture of Kerala for the verification of
some of the mathematical results(66)
"
4
Further, several treatises on architecture were
formulated during this period. Tantrasamuccaya of Cenn~s
N!r~yanan Namboothir ippad (A. D .1428), Si lpara tna of trikumara
(16 th centu ry) , Vastuv idya (Anm. ) , Manu ~yalayacandr i ka of
Thirumangalath Neelakant;.han (16th century) etc, are some of
the we1lknown architectural texts of Kerala. These are
compilations of vastu principles composed in Sanskr i t verses.
The first two. texts deals with temple architecture and the
other two explains the details of domestic archi tecture of
Kerala. Here we mainly consider the two texts
Tantrasamuccaya and Manu~yalayacandrika. There are many
versions of Manu~yalayacandrika and most of them contain
about 245 verses arranged in seven chapters. But the one
which was published by the Kochi Ma1ayalabh~9a Pari~kara~a
Committee in 1125 M.E(56)contains only 173 verses without any
chapterwise classification. This may be considered as the \
earliest of all the commentaries on Manu~yalayacandrika.
One of the contributions of Indian mathematics to
architecture is the method of representation of numbers.
In v3stu texts, the system of representation of numbers is
a combination of Sanskrit names for numbers and the word
numerals (BhutasaQkhya system) with place value. The
Sanskrit names for the first nine numbers are eka, dvi, tri,
catur, pafica, ~at, sapta, a~ta and nava respectively. In word
numeral system, numbers are expressed by means of words as
in the place value notation which was developed and perfected
5
in India in the early centuries of Christ ian era. In this
system the numerals are expressed by names of things, beings
or concepts which are very familiar to the people and
therefore the system is also known as the bhGta saQkhya
system. Thus the words, !kaf:la, baQa and nanda represen t the
numbers zero, five and nine respectively. The ka tapayad i
system is also employed for representing numbers in
traditional architecture of Kerala. The terms used for
fraction are 'bh~ga' and lamsa l meaning part or portion.
The words padam, arddha~, and padOnam are used for denoting
1/4, 1/2 and 3/4 respectively. The fractions are frequent ly
employed in defining the proportionate measures of the
elements of the building.
The ratio and trairasika or Rule of Three (proportion)
play an important role in traditional architecture. The
e" different parts of a building are proportionate to each other
and hence, if the measure of anyone of the elements is
known, the measures of other elements can easily be arrived
at by proportion. The celebrated ratio known as 'the golden
ratio', belongs to the I arddh~dhikam' ratios in traditional
architecture. In a 'golden rectangle I, the ratio of length
to its width is approximately equal to 1.618:1 or simply
1.618. This is the limiting value of the fraction F n+l/F n I
where F denotes the nth term of a F ibonacci series (4) • The n
inclination of the roof (amippu) is def ined in terms of the
ratio of rise to the run by considering an elemental right
6
angled triangle of base of unit length. It is implied that
when the sides of a right triangle are increased
proportionately,
same.
the ratio of height to base remains the
Geometr ical principles are imp 1 ici tly made use of in
determining the cardinal directions and forming the square
vastumat;lQala on a si te. The vc§:stupuru~amat;l9ala, the
intellectual foundation of a building, is derived graphically
with respect to two perpendicular axes named Brahmasutra and
Yamasutra intersecting at the centre of the vastumat;l9ala.
The grid system and the vlthi systems are geometrical methods
of determining the exact position of the grhav~dika
(foundation). The geometrical constructions of a triangle,
rectangle, circle, hexagon and an octagon whose perimeters
are the same as that of a given square have contributed many
major results to mathematics. It is significant to note that
in these geometrical constructions (or conversions) the
perimeter is kept as a constant instead of their area. This
is due to the fact that the perimeter is considered as the
prime dimension of a vastu which defines the yOni, the vital
air (pr!Qa) of a building. This is one of the difference
of Kerala architecture from that of other parts of India.
Further, an independent method is derived for finding the
length of diagonal, approximately, of a square wi thout using
the Pythagoras theorem. Several approximations are obtained
by implication for ~f an irrational number which is the ratio
7
of the circumference of a circle to its diameter. Another
contribution is the implication of the value of another
irrational number 12. The idea of I imi t is impl ied in the
construct ion of the image of I inga (sival inga) . Apart from
these, various practical methods are formulated for
determining accurate dimensions of different types of rafters
by the traditional architects of Kerala (perumtaccans). The
principles of vastusastra were made available to the common
man through these local 'thaccans' and therefore vastusastra
was often known by the name "thaccus~stram" in Kerala.
The chapterwise content of the thesis is given below
Chapter I, deals with the domestic architecture of
Kerala. The selection of site, geometrical determination
of the cardinal directions, formation of square mar;tdala, the
grid system and the vithi systems for fixing the grhavedika,
the concept of marma, Vastupuru~amal)9ala, un its of
measurement, the concept of yon i, different types of "salas'
and vertical elements of a building are explained with
appropriate figures.
In chapter 11, ·an outline of the temple architecture
of Kerala is given. The characteristics of different types
of temples, construction of the garbhagrha, classification
of temples depending on their plan-shape, tal a (storey) and
8
perimeter, pancaprakaras, vertical components of a temple,
natyamaQQapam (kuthampalam) etc, are explained briefly.
Chapter I I I, gives various approximations to the
irrational number ~ implied by the architectural texts. The
value of ~ (approximate) assumed in the construction of
vrttapr~sada and in "Thaccus~stram Bh~~a" is 3.1416 which
is the (~sanna' value of ~ given by ~ryabhata I (b. A.D.476).
Another value impl ied in I Tan trasamuccaya' is 3.125
approximately, in the construction of gajaprstba shape.
Some other values adopted for ~ are 3.2 and 22/7.
Chapter IV explaines the ex istan ce of 'golden rat i 0'
in traditional architecture of Kerala. The method of
construction of natyamaodapa and its length to width ratio,
uddhidhikam ratios and 'golden ratio', construction of golden
•• etangle .and its properties, relation between the terms of
the Fibonacci series and golden rectangle, application in the
idol construction etc, are given in this chapter.
Chapter V explains the Ru le of three (t raira-si ka) and
its applications. Trairasika and inverse trair!~ika (vyasta
trairlsika) are given in detail. Theorems on similarity of
right triangles and their applications in determining the
inclination of the collarpin (vala) in roof construction are
explained with figures. Application of traira§ika in
determining the heights of the ridge from the level of the
9
wallplate (u t taram) and the corresponding leng ths of ra f ters
for different aviccil (pitch), determination of the length
of the side of an octagon, the lengths of rafters using
EttampramaQam (sth_Postu la te) and NaTampramal)am (4th_poS tu 1 ate) I
various proportions of ridgeheight to semiwidth etc. are also
included in this chapter.
Chapter VI explains geometrical construction of
various plan shapes adopted in the tradi tional archi tecture
and deductions of mathematical values which are used or
implied in them. The arch i tectural val ues ass igned to the
shapes of a square, circle, vrttctyatam (elongated circle),
gajaprstl;ta (apsidal) and the methods of construction are
given in detail. The practical method of determining the
approximate length of the diagonal of a square without using
Pythagoras theorem and a very close approximation to J2 are
explained. Further, the methods of construction of a
triangle, rectangle, hexagon, octagon and circle each of
which having the same perimeter of a given square and the
method of inscribing an octagon in a given square are
included in this chapter. The method of construction of
'Sricakram', geometrical method of determination of lengths
of different types of rafters and the demarcation of lamba
and vi t'!na (vertical 1 ine and horizontal 1 ine) on them are
also explained in this chapter.
A translation of 'Manu~yalayacandrika' in English
language is given at the end of this work as an appendix.
Chapter I
RESIDENTIAL ARCHITECTURE
1.1. INTRODUCTION
Residential or Domestic architecture forms an
important branch of V~stuvidya. It is produced for the
social unit: the individual, family and their dependents,
human and animal. It prov ides shel ter and securi ty for
the basic requirements of life and Vastuvidya is the
ancient rnd ian knowledge of plann ing I des ign ing, bu i Id ing
and maintaining artefacts to meet man's physical and
metaphysical needs.
The word vas tu is derived from the Sanskrit root
( ~ ) 'vas t which means 'to
covers the earth suitable for
the buildings for different
dwell'. In general, it
human habitation (Bhami),
activities (Harmya), the
movable artefacts required for human use and conveyance
(Sayana and YSna). The principal vastu is of course the
Bhumi, others have been included as they rest upon the
BhOmi and are also used for resting upon.
There are several texts on Vastusastra which deal
with the residential architecture of Kerala. 'vastuv idya'
and 'Manu~yalayacandrika' are still used as reference
11
texts on residential architecture. Though they are
compilations of vastu principles which were prevalent
before 15th centu ry A. D. , they def ine a un ique style of
architecture which is harmoniously blending with the
geographical and climatic conditions of Kerala.
1.2. SBLBCTION OF SITE
For the construction of a building which is a
residence for man or god, the first and foremost
requirement was considered to be the sel ect i on of site.
The characteristics of
Manu~yalayacandrika{56}.
an
The
ideal
site
site is given in
must be suitable for
the living conditions of human beings, animals and plants.
'lb. presence of fruit-bearing trees, flowering plants and
__ inal herbs, gentle birds and animals, fertile soil,
und.~round spring and congenial climate were considered
good omens in the selection of the best site.
Sites of irregular shapes, like triangular,
al:eDpted, segmental and circular were to be avoided for
~ruction
~red.
of
In
houses and
the case
rectangular shapes were
of scattered settlements
(a..bh~agrima) as in Kerala, the location and extent of
the aite was often not so rigidly restricted. But there
were restrictions in constructing houses in agricultural
12
fields, mountain slopes, and very close to hermitage,
temple, river and sea. Mounds and depression may require
extensive levelling and may cause water logging or
drainage probl ems. A gentle slope towards north or east
was recommended in Vas tu tex t s. Before the construction
work is to be started, the soil is to be examined by
taste, colour, touch, and smell, by the trees standing
thereon, by the situation of the underground spring, by
birds and animals that frequent there and by the test of
germination of seeds in the soi 1. ManU~yalayacandrika(54)
prescribes simple experiments to ascertain the qualities
of the soil like ferti 1 i ty, humid i ty and compactness. The
imperviousness of the substrata could be tested by pouring
water in a pit of 1 Hasta (72 cm) square and 1 Hasta depth
~and watching the fall in the water level • An intelligent
. ,:!,'Stbapati' (traditional architect) can detect the hollow
ground made by termites or rodents by gently "tapping"
the ground by foot and listening the sound. Thus the site
is selected accordingly and the ground is levelled and
cleansed properly. Then the next step in the process of
construction of building is the determination of the
cardinal directions for the correct orientation of
buildings and roads in the site. 'Tantrasamuccaya' and
'Manuqyalayacandrika' provide geometrical methods based
on solar path and shadows.
13
1.3. SOLAR PATH AND SHADOW MBTHOD
This
solarpath (56) .
is a
In
geometrical method
this method a pole
based on the
(sanku) of height
~ Hasta (36 cm) is fixed vertically on a properly levelled
ground.
equal to
With the foot of the pole as
1 Hasta a circle is drawn on
centre and radius
the ground. The
points where the shadows of the tip of the pole touch the
circle in the forenoon and afternoon are noted. The line
joining these two poin ts gives the approx irnate East-West
direction. To get the correct E-W direction at a place
the following procedure is adopted.
The shadow of the tip of the pol e does not fall
at the same point on the forenoon of the subsequent day
due to the northerly and southerly declination of the Sun
(Uttarlyanam and Dak~inayanam). This point will be to
the south or to the north of the shadow point in West,
noted on the first day, according as the Sun is in
Ottarayana or Daksinayana. In ei ther case the arc-length
between these points is trisected. The point of
trisection nearer to the first day's shadow point is
joined with the shadow point on the East side to get the
correct W-E direction as shown in Fig.l(a).
l3(a)
DIKNIRANAYAM (SANKUSTHAPANA METHOD)
5
Fig.l(a)
W1 · Tip of the shadow of the Sanku on first day · "2 • Tip of the shadow of the Sanku on second daY2 •
r,- · Peg · 11 · Evening shadow point on first day · Pll : Radius of the circle
I" · Bast-West line · SR · South-North line ·
14
The argument behind this correction is that the
displacement of the points on West side is due to the
movement of the sun Southward or Northward during the
twenty-four hours that have elapsed between the two
markings in the forenoon. The actual correction that is
necessary is for the displacement between the markings
of the forenoon and afternoon, ie, for about 8 hours.
The forenoon marking therefore is shifted by one-third
of the total displacement for one whole day and that is
connected with the point for the afternoon.
1.4. PORMATION OF THE SQUARE MANDALA
The line in the W-E direction is known as the
ec.hmaeutra. To determine the S-N direction. consider two
. ~.l intersecting circles with their centres on the
BrahmasOtra. The line join ing the poin ts of intersect ion
-of the circles will give the S-N direction. This line
is called the Yamasutra and the point of intersection of
the Brahmasatra and Yamasiltra is named as the Brahmanabhi
(origin).
With respect to these axes the boundaries of the
.ita were demarcated to form a square of required
dimensions. The diagonals of the square are known as
'Kar~asQtras' •
15
It is to be noted that the requisites for selection
of site for a domestic building are different from the
requisites for other buildings since the functions of a
human residence are en t i rely di f feren t from the funct ions
of a temple or such other buildings.
1.5. LOCATION OF A DOMESTIC BUILDING
If the size of the site is small (ie, between
168 x 16H and 32H x 32H), the entire site is taken as the
house-plot (g~hamaf}9ala) (58). If the site is of large size
then it is divided into four quarters (quadrants) by the
Brahmasutra and Yamasutra. The N-E quadrant named as
manufyakhaQ9a and the s-w quadrant called as devakhaQ9a
are taken for gFhamal)9a1a. If the size of the KhaQ9as
a&fe still large, these two khandas are again subdiv ided
into' 4 upakhaf}Qas and the s.w upakhaJ?9a of the
.anufyakhaQ9a and the N. E upakhaQ<;'1a of the devakhar,JQa are
taken as grhama~Qala.
1.6.1. DBTERMIWATIOR OF G~BAVEDIKA USING GRID SYSTEM
In the grid system (or Padaviny~sam), the square
maQ(ja1a is divided
Manu,yl1ayacandrika
into a grid of
prescribes A~tavarga
cells (Padas).
(8 x 8) ,
Navavarga (9 x 9) and Dasavarga (10 x 10) types of grid
16
systems for the planning and design of houses, maQ9apas
etc and Navavarga is considered to be more acceptable than
others. The mapdala determined by 9 x 9 grid system is
called the Paramasayika maQqala. It is defined by 10
lines each in the W-E direction and S-N direction
producing 81 cells (Padas)
centre, the region of 9
of Brahma where all kinds
in the square maoQala.
cells is called the
of constructions are
In the
pada
to be
avoided. Surrounding this region is the region covered
by two envelopes of square cells which is def ined as the
space for const ruct ing the S~las (homes). The ou termos t
envelope of square cell s def ines pos i t ions of subs id iary
constructions like cattleshed, well, tank, kitchen etc.
With respect to the Brahmapada, four side spaces
and four corner spaces are available for building Salas
(homes). The width of the spaces is the measure of 2
cells (Padas) and the length is the measure of 2, 3, or
4 cells depending on the vastu divisions of 8 x 8, 9 x 9
or 10 x 10 grid systems respectively. The corner spaces
are square spaces wi th side of the measure of two cells.
In the case of 9 x 9 grid system, the total ground
coverage is restricted to 40 out of 81 cells or a little
less than 50 percent of the grhamaOQala and this is
acceptable according to the modern building code also.
17
The outermost cells form a permanent open space around
the building, having a width equal to l/9 th of the
site-width (57) .
1.6.2. VITHI SYSTEMS
In vithi system, the site is divided into 9 vIthis
or concentric square envelopes around the B~ahmanabhi,
which is the point of intersection of Brahmasutra and
Yamasiltra. The innermost vithi is known as the
Brahmavithi. The other envelopes around the Brahmavlthi
are named as Vinayakavlthi, Agnivfthi, Jalav Ith i,
Sarpavithi, Yamavrthi, Kub~ravrthi , D~vavithi and
Pi~acavlthi in order. The width of the vithi depends on
the length of the al)kalja or t~lam, the height of owner
of the house. Suitable mUltiples of this length is taken
as the width of the v I t h i and the reg ion comprising the
BrahmavIthi and Gan.~avlthi is considered to be the
appropriate space for the gfhav~dika. If the site is too
small then the grhavedika is determined by combining
the Brahmavithi, Gane~avithi, Aqnivithi and Jalavithi.
In any case the outermost envelope, the pisacavithi is
to be avoided for construction of madn building . ... ">.--<
There is another method of dividing the site into
four vrthis, namely, Brahmavlthi, Devavithi, Manu~yavIthi
18
and PHsacavlthi. The reg i on compr is ing of Dev av It h i and
Manu~yavrthi forms the buildable area of the building.
This method is used where the site is small.
Both the grid system and Vlthi system broadly give
the same floor area coverage leav ing the inside courtyard
and the outermost peripheral envelope.
1.7. THE CONCEPT OF MARMA
The set of orthogonal lines dividing the
VastumaQQala into grids are known as nadis (padasutras)
and the diagonals of the square maOQala are known as
Rajju. The lines parallel to these Rajjus (Kaqla Sutras)
and .. passing through the corners of 3 cells, or 6 cells
are also known as Raj jus. The nodal points of the n~9 is
and diagonals (Rajjus) are called 'marma' (57). Out of these
100 murmas, there are 4 important murmas called
rMah~marmas' [Fig.l(b)~ A t the points where two na9 i sand
two Rajjus intersect constructions such as wall, pillar
etc, are to be avoided. The rule stipulates that
constructions can be done on either side of the nodal
points leaving half the width of the sutra on either side.
Matlufyalayacandrika defines the width of the sGtra as
1/12, 1/8 and 1/16 of the dimension of a pad a (cell) when
the VAstumal}Qala was d i v ided in to 81 padas, 100 padas and
18(a)
SALAS AND MAHAMARMAS
KarnnaSUtra , -
~*--~ ___ Rajju
i
Navavarga (9 x 9 pada) System
.. ·Mahamarma * Marma
"',1- Nadisandhi fi:' Karman tam )( Rajju sandhi ~ Rajju Nadi Sandhi
Fig.l(b)
E East Sala S South Sa la W : West Sala N : North Sala NE,SE,SW,NW : Corner Sala
19
64 padas respectively.
These marmas or nodal points are important because
they def ine the exact posi t ion of the bu i Id ing in the
Viistumao9ala. The Mahamarmas may be used as the referral
points for further constructions, rectifications and
repairs of the building in future. Hence the
intersections (vedha) of any element of the building with
these points are to be avoided.
1.8. "lHE CONCEPT OF YASTUPURU~A
The vastumaQQala is divided into 81, 100 or 64
cells. Then 45 regions (padas), one at the centre, 12
in the surrounding two envelopes and 32 in the outermost
envelope, are determined and 8 positions outside the grid
are also defined. These 53 positi.ons (padas) are called
by the names of 53 deities. Now a two dimensional
figure of a man is superimposed on this square maQQala
in such a way that he 1 ies along the KarQasQtra wi th his
head in the N-E corner and legs in the S-W corner. Thus
~the square VastumaQ9ala becomes the Vastupuru9amaQ9ala
,Wiich is symmetric about the Karoasutra and the size of
~e Vastupuru~a varies according to the size of the
Yletumar;tdala. . But the relative positions of the spaces
in a V~stumal}<;'lala will not be changing and this property
20
enables to bring a standardisation in the positioning
of different spaces in a building. Hence the
Vlstupuru~amaOQala is the metaphysical plan of a
building, a temple or a site plan of a house which
completely defines exact positions of specific spaces
in a building and is closely related to Vastuma~9ala
based on grid system (Padavinyasam).
1.9.1. UNITS OF MEASUREMENTS
Measurement is an important factor for any
architectural construction. A system of measurement
developed from a basic unit is called a scale. At
different stages of construction the necessity of small
and large measures will occur and the scale is to be
selected in such a way that it su its the requ iremen ts .
The early linear measurements indicate that the units
of linear measurements used were mainly derived from the
parts of the human body. The finger, the palm or hand-
breadth, the foot and the cubit were the principal
•• aaures. The anthropometric module of one vyama (span)
:j.. -divided by 8 to give a pada. Angula was considered
" .. the smallest practical linear measure in ancient
India. Eight angulas define a pada.
·flt :
21
1.9.2. UNITS IN RANU~YALAYACANDRIKA
Manu~yalayacandrika defines 3 types of angulas
based on the measure of 8 yavas I width of 8 Navara grain
and length of 4 Navara grain. Each type is again
classified into 3 categories of Uttama (good) I Madhyama
(medium) and Adhama (bad) depending on the number of
seeds. The smallest unit of measurement is called
Param~nu (smallest .atom) which is defined as the size
of the minute aerosol particles seen in a dark chamber
when the sun I s rays creep into it. The units which are
the multiples of this unit are given below(13).
8 Paramanu 1 Trasarenu or Ratha dhuli
8 Trasarenu 1 Romagra
8 Romagra 1 Liksha
8 Liksha 1 Tila ( Yu ka) : (0.47 mm)
8 Tila (Yuka) 1 Yava 3.75 mm
8 Yava 1 Angula 30 mm
8 Angula 1 Pada 240 mm
3 Pad a 1 Hasta (Kol) : 720 mm
8 Pada 1 Vyama 1920 mm
Thus it is possible to unify the two dimensional
system, one based on grain size and the other based on
human size.
22
The measure of 24 angu la (72 cm) is the standard
Hasta which is known as Ki~ku, Aratni, Bhuja, or Kol.
By successively increasing the length of Ki~ku by 1
angula each upto 31 angula there will be 8 types of Kol
(cubit) and each is used for specific purposes. Thus
the 9 types angulas give rise to 72 types of Kols. The
measure of 4 Kols is defined as a daQdu and 8 daQdu
produces a Raj j u wh i ch is 1/100 th of a yojana. The octal
system is used in defining the units in traditional
architecture which may be used in computers easily.
In traditional architecture of Kerala incorporates
different scales to serve measurement at different levels
of uses. The perimeters of quadrangle (courtyard), well,
tank, houses etc, are measured in Kol. Door, seat
(pidam) etc, are measured in Angula and Ornaments are
measured in Yava where as clothes are measured using
Vitasti (Mu~ham). Weapons and other small quantities
are measured using by breadth of fingers and Mu~ti. The
perimeters of the viII age, town, city etc I are determined
by daJ;ldu.
1.10.1. THE CONCEPT OF yONI
Yeni is an architectural device which defines a
proper orientation and dimension of the vastu. For
23
buildings (for domestic or temple) yoni is considered
to be the vital air (pr~Qa). with respect to the
Brahmapada, a g Fhav~stu can take eight posi t ions four
in the cardinal directions and four in the corner
directions. These positions and directions are
considered to be the birth places of the vastu on earth
and denoted by the names Dhwaj a, Dhiima, S imha, Kukku ra,
VF~abha, Khara, Gaja and Vayasa in eight directions from
the East direction onwards in cyclic order.
In VastusSstra, the orientation of the building
is defined from its prime dimension. Regarding the prime
dimension there are differences of opinion.
I Brhatsamhi ta', recommends the area, Raj avallabha accepts
the height, Manal!Ara pt"escr ibee the width,
Tantrasamuccaya and Manu~y~layacandrika adopts the
perimeter as the prime dimension of the vastu. The
method of finding the y~ni is given in
Manul?y~layacandrika(54t chapter 3, verse 30) as "I~tatana
vitana mana nicaye trigne/iltabhir bhajite ~es(:) y~ni" I
i e,
mUltiply the perimeter by 3 and divide it by 8. Then
the remainders will represent the 8 yonis. Thus if P
is the perimeter then 3P:::8q+r where q is the quotient and
r is the remainder, which varies from 1 to 8 (0). When
r=1, the yoni is known as Dhwaja and it defines the
24
orientation of the building on the East side of the
Brahmapada (or Ankar;ta). If r=2, it represents DhGmayoni
in S-E direction. Similarly, all the other six yonis
are def ined. Since the vastu var ies from large to small,
the basic units of prime dimensions also vary with the
size of the vttstu. For the computation of yeni
in different perimeters
perimeter
are
of a
expressed
building is expressed in
units.
Hasta or
The
Kol
whereas the perimeter of a door is given in angula and
the measure of details are presented in Yava.
In the case of 'gFhavastu, the least perimeter
of Dhwajayoni is 3 Kol which is equal to 9 padas. (8
angula = 1 pada and 1 angu la = 3 cm). Simi lar1 y the
least perimeters of
15 and 16 padas
perimeters are got
other yon i s are 10,
respectively and
by incrementing 8
11, 12, 13, 14,
the subsequent
padas to each
category of perimeters. Thus the yoni system classifies
the perimeters into eight categories and each of these
eight sequences of numbers form an Ari thmetic Progression
with first term as the least perimeter and the common
difference 8 pada in the case of buildings. This system
of numbers may be represented on an Archimedian Spiral
of an initial radius 3 Ko! (cf. Fig.l(c».
24(a)
ARCHIMEDIAN SPIRAL OR YONI SPIRAL
N 31
27
S
Fig.l(e)
l. E.
2. SE.
3. S.
4. sw. 5. w. 6. NW.
7. N.
8(O)NE.
DHWAJA ¥ONI
DHUMA YONI
SIMHA YONI
KUKKURA YONI
VRSABHA YONI
KHAM YONI
GAJA YONI
VAYASA YONI
25
1.10.2. MODULAR COORDINATION IN TRADITIONAL ARCHITECTURE
Originally, the y~ni concept was formulated for
determining the orientation of the grhavastu and to
standardise the construction of buildings. But later
ycni was attached to all artefacts, fixed or movable.
The standardisation in the building construction was
attained by selecting a small basic unit of size or
module in the horizontal direction. In the traditional
architecture, the basic module adopted was the minimum
thickness of the wall which was about 1 pada (8 angulas).
This module has a greater significance in Kerala than
in other parts of the land because here the prime
dimension is accepted as the perimeter which should be
a multiple of pad a so that when it was divided by 8,
leaves integral remainder. Further it is stipulated that
for any building the prime dimension could be taken as
the perimeter measured along ins ide, cent reI ine or
outside the walls(54). It was considered auspicious that
both the inside and outside perimeters yield the same
ymt i number. This is possible only if the wall thickness
is 8 angulas (1 pada) or multiples of it. I t is to be
noted that in ancient times the size of the brick was
8x4x2 angula (58). This module may be derived from the
height or span of a man as a reference measure which is
equal to one Vyama (;;;; 8 pada). Hence 1 pada is the most
26
appropriate basic size to be considered as a module. For
vastus of smaller sizes, modules of preferred sUbunits
are accepted. Thu sit is ev iden t tha t the modern idea
of modu 1 ar coord ina t ion was not a novel concept to the
traditional architecture of Kerala.
1.11. RETHODOF PINDING PERIMETBR AND LENGTH
Methods of finding the perimeter when the
appropriate length is given and the length when the
perimeter is given are explained in . (54)
Manu~y~layacandr1ka
(chapter 4, verse 2-4) • According to this method, if
P is the perimeter (in kol and angula), 1 kol is the
chosen length, y the yoni number then
P = (8 1 + y)/3
and 1 = (3 P - y)/8
Another formula for P is given _ . (54)
(Manu~yalayacandr1k~
as P = 2 1 + 2 1 + y which can be reduced to the 3 3
first ·one.
For determin ing the y(5n i corresponding to a
perimeter of a bu ild ing, t he per imeter is to be expressed
in Padas (1 Hasta = 3 Pada). In texts on traditional
architecture, tables of perimeters of buildings belonging
27
to each yoni are given in Hasta (kol) and angula units.
Here the angulas are in mul t ipl es of 8 (i e. 8 angula or
16 angula). Even though there are 8 classes of
perimeters representing the eight yonis, four of them
are not accepted for houses. They are the per imeters
representing the corner yOnis or the perimeters of even
number of padas. Sometimes the y~nis are represented
by the numbers 1 to 8. For buildings, only the prime
dimensions yielding odd yoni numbers were preferred.
Further, even these perimeters
astrological canons (Ayadi~a9varga)
were restricted by
as ut tama, madhyama,
or adhama. Thus the words, "y~ni: praQa ~vadh§m-n§m~
about yOn i becomes true since it def ines the or ienta t ion,
the basic module of the prime dimension and dimensions
of all other elements of a building.
1.12.1. PROPORTIONS IN TRADITIONAL ARCHITECTURE
In traditional architecture proportion plays an
important role in the construction of buildings from the
The qualities like
horizontalness, verticalness and stability of an object
to the last plate. foundation
are produced
(. gfhavt!dika)
of the plot
by
is
and
the proportion. The buildable area
determined in proportion
it is so stipulated that
to
the
the area
ratio of
28
the bui 1 t area to the area of the plot must be less or
equal to hal f • For domestic buildings, rectangular
shapes are accepted and the dimensions of width and
length are compu ted from the pr ime dimension (per imeter) •
Manuljly§layacandrika prescribes three methods for finding
the width,
method.
namely,
1.12.2. GU,i8SA METHOD
padayOni, i~tadrrga, and gUl)am!>a
In gunamsannethod the semiperimeter of the building
is divided into 8 to 32 equal parts and in each case the
width is fixed as the measure of 4 parts and the measure
of the
building.
remain ing parts becomes the 1 ength of the
Here, the ratios of width to length are
divided into four categories.
integral mul t iple of width,
When the length is an
the ratio is known as
Samatata. If a quarter of the width is added to this
length, then it is known as padadhika, and when the
length is increased by half the width, the ratio is known
as ardhadhika. If the length is diminished by a quarter
of the width (except in the 1 at case) in the samata ta I
it is called padona. Evidently, the ratio 1:1 of width
to length belongs to the samatata category.
WIDTH-LENGTH RATIOS
6 units
8 units
4 units
9 units
3 units
10 units
2 units
lO~ units
28(a)
Perimeter = 24 units
Width:Length = 6:6 = 1:1 (W:L)
Width:Length = 4:8 = 1:2
Width:Length = 3:9 = 1:3
Width:Length = 2:10 = 1:5
t' I Width: Length = 1"2 units 1~:10~ = ):7
~------------------------------------------~
Fig.l(d)
29
It may be noted that the ratios of width to length
of a rectangle varies from 1:1 to 1:7, the efficiency
of space enclosure decreases so that further ratios of
width to length are deleted, Fig. 1 ( d) . The four
categories of ratios are given below.
Samatata Padadhika Arddh~dhi ka Padona
1:1 1:1.25 1: 1. 5 1: 1. 75
1:2 1:2.25 1:2.5 1:2.75
1:3 1:3.25 1:3.5 1:3.75
1:4 1:4.25 1:4.5 1:4.75
1:5 1:5.25 1:5.5 1:5.75
1:6 1:6.25 1:6.5 1:6.75
1:7
It is stipul a ted, wi thou t any ev iden t reason I that
the ratios of padona are not acceptable for any building.
1.13. TYPES OF SALAS
Manu~yalayacandrika describes nine types of central
courtyard houses. Basically they are divided into two
types - separated salas (Bh inn a salas) and non-separated
Brahma Sutra
BHINNA 'S~IA
w
Patinjattini
ABHINNA SALA
West Patinj
Corner house
ttini
Corner house
29 (a)
BHINNA AND ABHINNA BALAS
The
Yama
North
ini
Vadakkini
ANKANA ,
Thekkini
South
Fig .l( e)
Sutra
Kizhakkini
Corner house
East
Kizha cl<. ini
Corner house
30
s~las (Abh inna sa-Ias) [F ig.l ( e )1. If the four side- houses
(diksalas) stand separa ted around the
a~kaQa) satisfying the conditions such
width etc, prescribed for each of them,
courtyard (or
as yoni, gati,
it is called a
(diks~nas) are I Bhinnasala I • When the four side houses
structurally combined as one
corner houses (vidiks~las)
Depending on the methods of
sid6houses
unit together with the
is called Abhinnasala.
joining the roof
and corner- houses
frames,
using interconnecting the
passages (aliodas), and
again Abhinna s~las are
computation of
classif ied into 8
yoni etc,
types so
the
that
there are 9 types of catussalas in total.
In Kerala the catussala is known as Nalukettu,
generally built for the elite group, which is a
combination of four side houses along the four sides of
the centralyard, or nadumuttam. This form is extended
horizontally to Ettukettu, Patinarukettu etc, by
adjoining suitable number of courtyards or vertically
by const ruct ing su i tabl e number of storeys (tala) exactly
as that of the ground plan. Depend ing on the needs, one
may build anyone of the 4 salas (Eakasala), a
combination of two (dvis~la) or a complex of three
(Trisala) according to the rules stipulated in the
Vastusastras. The common type of s~Ua (house) accepted
31
in Kerala is the Ekasa1a which consists of a core unit
containing three rooms connected to a front passage
(Alinda). This may be extended horizontally by adding
corridors on four sides and vertically by constructing
upper storey.
1.14. VERTICAL BLBMENTS OF THB BUILDING
The height of the building from the ground level
upto the level of wallplate (Ut taram) is termed P§damana,
which is taken
The height of
equal to or proport iona1
the foundation (adhi~tana)
to
is
the width.
a fraction
of the padamana and the thickness of the wall is also
proportional to the p~damand. Deleting the height of the
adhi~tana from the p~damAna gives the height of the
pillar. The wall is topped wi th the wallpla te (Ut tara)
which is considered to be the most important (Uttarn~nga)
component of a building. The uttara (wallplate) is placed
over the pOt ika at the upper end of pillar. There are
three types of ut taras namely, KhauqOt tara, Pa throt tara,
and RupOttara (the definitions are given in the glossary)
depending on the thickness of the uttara in relation to
its width.
32
The roof frame consis ts of ridge (mOntayam) ,
rafters 'and the ut taram (wallplate) or the arih}am. The
rafters are held in position by collar and collar pins.
(Bandam;, and Vala). The rafters are seated on an
additional annular wooden member (cittuttaram). The
indiv idual elements of the building are fabricated
independently and joined together in position by using
wooden wedges.
by removing the
be reassembled.
The individual members can be dismantled
wedges wi thou t damage to them and may
The pi tch of the roof is taken as 45 0 •
The Perumthaccans of Kerala were responsible for the high
degree of perfection achieved in construction of
traditional buildings.
*********
Chapter 11
TEMPLE ARCHITECTURE
2.1. HISTORICAL BACKGROUND
The history of archi tecture is concerned more wi th
religious building than with any other type because in
most civilizations the univer8al and escalated appeal
of religion made the church or temple the most
expressi ve, the most permanent and the mos tint luent ial
building in any community. In India temple was
considered the residence of the deity and it is the most
significant and typical monument of Indian architecture.
The earlier shrines were simple enclosures or plain
structures 1 ik~ .. p~a tf orm wi th or w i thou t a roof. The
elaborations of the temple structure followed the firm
establishment
development
crystallise.
of
of
image-worship
the ritual,
and
which
the accompanying
took time to
In Kera1a the earliest temples so far discovered
date from the eighth century A. D. The Kulasekhara period
(800-1102 A. D.) marked the rapid establ ishment of templ e
complexes and Kerala's peculiar temple architecture owe
much resemblance to N1Hukettu and Ettukettu of the
34
traditional houses (2) It attained perfection during
the late medieval and early modern periods. Several
vastu texts were formulated during this period and
'Tantrasamuccaya ' of C~nnas Narayanan Namboothirippad
explains the compl ete detai Is of templ e const ruct ion and
the methods of offerings to seven deities in 2896
sanskrit verses comprised in 12 chapters. The first step
in the construction of temple is the selection of
appropriate site.
2.2. SELECTION OF SITE FOR A TBMPLE
The sites for temples are described in
Tantrasamuccaya elaborately. They are defined on the
h ill tops, on the banks of rivers and seas, along lakes,
near the holy waters, grooves of trees and such other
locations which will prov ide mental happiness and peace.
The sites of types of Supadma, Bhadra, and Poorna are
auspicious for temples whereas the type of 'Dhumra ' is
inauspi c i eus for the pu rpose. The sites for temples in
villages or cities may be located at the centre or at
different positions according to the nature and power .. of the dei ty.
35
After selection of appropriate site, the soil is
to be tested for its compactness as in the case of
domestic buildings and sanctification of the site should
precede temple construction in accordance with the
stipulations given in the texts.
are to be determined accordingly.
The cardinal directions
2.3. GEOMETRICAL METHOD OF DETBRMINING THE CARDINAL
DIRECTIONS
For the determination of the cardinal direction~
a simple geometrical method is given in Tantrasamuccaya.
Here also, consider a wooden peg (~~nku) of length half
hasta.
ground.
It is fixed vertically on a properly levelled
Draw three concentric circl es wi th radii lz, 1
and llz hasta respectively and with centre at the foot
of the saoku.
of the "Saoku
The points at which the shadow of the tip
just touches the circles are marked on the
circles. Then, with these points as centres draw three
circles having radii equal to lz hasta. The two lines
through the points of intersection of the circles will
meet at a point and the line joining this point and the
foot of the ~aQku will determine the North-South
direction. The perpendicular line will represent the
East-West direction as given in Fig.2(a).
35 (a)
SANKU-SHADOW METHOD (AS GIVEN IN TANTRASAMUCCAYA)
S-N
Sanku
Circle
Circle
N
S Fig.2(a)
of height 12
with radius
with radius
with radius
angula
12 angula
24 angula
36 angula Circle Tips of the shadows on the circles (Centres of equal circles) south-North direction
36
2.4. CLASSIFICATION OF TEMPLES
Temples are classified from different viewpoints
such as thei r size, number of storeys they possess and
their regular shape in des ign . According to their size
they are broadly treated under two heads, known as
Alpaprasada and Mahaprasada.
classified as Jati, Chandas,
Mahapras~das are again
V ikalpa and 1\bh~sa (15) .
Depending on the number of storeys they are named as
Ekatala, Dv i tala, Tri tala etc, and on the bas is of thei r
shape and design they are classified as Caturasra
(square), Catura'Sradirga (rectangular), Vrtta (circular),
HastipF~~ha (apsidal), Vrttayata (elliptical), 9adkone
(hexagonal), and A~ta§ra (octagonal). In Kerala, most
of the temples are of the Alpaprasada cl ass and those
under the Mahapr~sada class are very few in number.
Based on the regional styles, temples may be classified
mainly in to three types N~gara, Vesara and Drav i9 a (15) .
This differentiation is made from the point of view of
shapes and their combination. N~gara is purely square
throughout from the basement to the finial: but with
regard to Drav i9a and V ~sara, the shapes may be both pu re
and mixed. The shape of the Dravida shrine may be either
purely octagonal or octagonal mixed wi th square and the
shape of v~sara temple may be either wholly circular or
combined with square.
37
2.5. ALPAPRASAoA
In Kerala most of the temples belong to
Alpaprasada class. This class varies from a beam
(uttara) length of 2 hasta 18 angula to a beam length
of 15 hasta 10 angula and correspondingly the perimeter
varies from 11 hasta to 61 hasta 16 angula. Their widths
are grouped into 3 hasta type, 4 hasta type etc, each
width differing from the other in the measure of 8
angulas. Temples which come under the type of 3 hasta
(comprising the widths 2 hasta 18 angula, 3 hasta 2
angula and 3 hasta 10 angu la) w ill have pi lIars measur ing
2 hasta for their height and f or that of 4 hasta type,
the height will be 2 hasta 4 angulas. The height is to
be increased by 4 angulas for each type of temples in
the increasing order upto a maximum of 4 hastas.
The total height of a temple from the lowest
member (pC[duka) of its basement to the finial (stupika)
is prescribed in the following 4 ways. The height is
proportional to the breadth (or width) and is defined
3 3 as 1 - B, 1 ~ B, 1- B
7 4 or 2 B where B represents the
breadth.
38
2.6.1. GARBHAG~HA
The garbhagrha occupies the central portion of
a temple complex
such as Agrasala
Upadevalayas etc.
if the prasada is
containing other accessory structures
(halls), NatyamaQ9apam (Kuthampalam),
Garhbagrha is of square shape even
of circular, octogonal or of other
shapes. The width (breadth) of the garbhagrha is
determined in proportion to the width of the prdsada.
In tan t rasamu ccaya, the n in e proport ions are 9 i v en
as 2/3, 3/5, 4/7, 5/9, 6/11, 7/13, 8/15, 1/2 and 5/8 of
the breadth of the prasada.
2.6.2. THE THICKNESS OF THE WALLS
The thickness of the wall of the garbhag~ha is
one-eighth of the width of the garbhagrha and the
thickness of the wall of pr!s~da is defined as one-eighth
of the width of the pras~da. The passage between the
two walls is the Nadi (Etanazhi). If the structure is
too small, the two walls are combined into one thick
wall.
39
2.6.3. THE DISPOSITION OF GARBHAG~HA
In the case of Alpapr~s~da divide the length and
breadth of the prasada each into 5 equal parts forming
25 padas. Then the central pada will form the
disposi tion of the piFha or pedestal of the seat of the
dei ty (Murth i) • The immed iate eight quarters tha t
surrounded the
The sixteen
central
quarters
pada will form the
that surrounded
garbhagr ha .
beyond the
the thickness garbhagrha will provide disposition
of the ghanabhitti or thick wall.
for
In another method(15) , divide the length and
of
The
breadth
padas.
eight padas
the prasada into nine parts
innermost pada prov ides for
surrounding will constitute
each
the
forming
pitha,
81
the
the garbhagr ha •
the division The
for
surrounding 16 padas
wall, the
will constitute
the inner wall of garbhagr ha • The
outermost padas will provide for
The space between the two walls
(Etan~zh i) .
the wall of pr~s~da.
is known as the N§di
2.7. VERTICAL COMPONENTS OF A PRASADA
In general,
namely, Adhi~tana
there are six main
(basement), pada
parts of a temple,
(pillar), Prastara
40
(entablature), Gala (neck), 'Sikhara (roof), and Stupika
(f in ial). The Kerala temples in thei r simplest form have
only the four essential parts instead of six of the
simple vimana (temple). The Prastara and Gala (grlva)
below the 'Sikhara are avoided. These parts bear fixed
and relative proportion to one another.
The Adhi~t~na (base) is the lowest portion of a
building. It is the strongest, firmest and the most
solidly built, and carries the weight of the remaining
parts of the structure above. Adhi~tana is classified
into different types on the basis of difference in
dimensions of its mouldings or the presence or absence
of one or other of its mould ings. The various mouldings
of the adhistana are P~duka, Jagati, Kumuda, Gala,
Antari, Kampa, Pattika or Patta, Prati and Vajana. There
are four types of adhistanas explained in
Tantrasamuccaya (15) as given below.
41
Height of the Adhi~t~na is divided into
(a) 24 parts (b) 21 parts ( c) 12 parts (d) 12 parts (Pratikrama) (padabandha)
Paduka - 3 Paduka - 3
Jagati - 8 Jagati - 7 Jagati - 4 Jagati - 4
Kumuda - 7 Kumuda - 6 Kumuda - 4 Kumuda - 4
Gala - 1~ Kumuda Kumuda Kumuda 5
Pat i 1 Pa~i 1 Pati 1 - - -
Kampa - 11 Gala with Gala - 1 Gala - l~ 5 Pada - 2
Gala - li Gala Pati- ~ Vajana - 1 Vajana 5 with Pat i - l~
Pati - l.!. Pati with Pat i - 1 5 Vajana - l~
Total - 24 Total - 21 Total - 12 Total - 12
The garbhagrha is constructed on the adhi~t8na.
Among the structural divisions of a temple, the
columns come above the Prati and below the Uttara
(Wallplate) • The pillars are spaced at equal intervels
apart so that the weight supported is equally distributed
among them. Col umns d i ff er in their shapes and
architectural ornamentations. Geometrical shapes like
square, octagonall sixteen-faced and circular are used
42
in the construction of pillars. Pillars of mixed shapes
are constructed depending on the type of prasada.
The sikhara corresponds to the roof of the temple
or garbhagrha. In small temples, the garbhagrha and the
prasada will be the same and the garbhagrha will have
corbelled roof. The inner side of the garbhagrha being
made into an octagon by putting up corbels at the corners
from above half the height of the door and gradually
clossing the gap wi th stones, or br icks accord ing to the
I Kadal ikakarana I process (16) The he igh t of the ceil ing
from the level of door will be half the width of the
garbhagrha.
To construct the roof of the temple, the rafters
are to be so placed that their lower end must rest on the
uttarapattika, while their upper extremity must be secured
on a kuta of suitable shape and dimensions. Then the
rafters should be covered all around with wooden planks
or metal-sheets. Tiles are used for covering the pyramidal
roof of wooden planks.
The ~ikhara is surmounted by a finial (StOpika).
It bears dis t inct proport ion to the he igh t of the temple
42(a)
VERTICAL COMPONENTS OF A SRIKOVIL
- --- S Jlll' ,
2 - - - - - - - S Il'\. H H k R;
--I-
2 - -- Bltl T TJ oR.. PILLtH<
• - ~ 7t.{) H I .s n·H1 N r~ , .
Fig.2(b)
43
and in general, its height will be equal to that of the
height of the basement (adhistana). It consist~ of 4
parts, namely, Padma (full-blown lotus), Kumbha (pot),
Nala (lotus stalk) and KU9am~la (lotus·bud).
2.8. VERTICAL PROPORTIONS
Tantrasamuccaya prescribes the simplest and most
commonly accepted proportions. The height of the temple
is determined in anyone of the ways as prescribed
earlier. Divide this height into 8 parts. Then the
(or wall), prastara, gala, height of adhi~tana, pillar
aikhara and finial will be given by 1 part, 2 parts,
1 part, I part, 2 parts and 1 part respect i vely. Thus
each element of the temple will be in the ratios
1:2:1:1:2:1 of the height of the temple (Fig.2(b». But
the height of the temple depends on the width of the
temple and hence each vertical component of the temple
is proportional to its width.
2.9. DISPOSITION OF THE DOORS
The main door of the sanctum sanctorum, is placed
in front of the image (deity). Divide the thickness of
the wall into 12 parts and mark I ine separating 7 parts
44
line. The door should inside and 5
be so placed
parts outside this
that the middle of the door must coinside
with the above line. There are other three doors known
as 'false doors' or 'ghanadvAras' on the other three
sides. They possess all the ornamental details of the
main door along with the decorations of T6ranas on their
upper side.
In front of
stone-steps (sopana)
the entrance is a flight
side-slabs
of
flanked by stone or
the balustrades, which contain rich relief
banister or coping being shaped in
elephant trunk issuing from a vyalimouth.
2.10. PARcAPRAKARAS
These are the bounding limits
surrounding the pr~sada or Srikovil.
sculptures,
the form of an
of five regions
These 1 imi ts are
defined in proportion to the width (breadth) of the
pras~da and
daQQu.
Madhyahara,
the outer-width of the pr~sada is known as
The Pancaprakaras, AntarmaQ9a1a, Antahara,
Bahyahara and Mary~da are determined at ~,
1 or l~, 2, 4, and 7 dalJQu from the ex ternal side of the
pr3sada accordingly, Fig.2(c). The AntarmaQQala and
Maryada are of square shape while the other three are
"
A. Pitham B. Namaskaramandapam C. Balikallu O. Prasada (Srikovil) 1. Antarmandalam 2. Antahara 3. Madhyahara 4. Bahyahara 5. Maryada
44(a)
PANCAPRAKARAS
~I'
r I I
I I
1 0
r' A mt. \.1-' -
, S
Fig.2(c)
nu L.J
.,
2 3 4 5
.r&. E L..J
45
of rectangular shape with front side elongation
(Mukh§y§mam) •
The innermost boundary line denotes the positions
of a~tadikpalakas. The namaskaramaQQapa is located
within the region of Antahara. The open court is
surrounded by a Nalampalam (or Cuttampalam) in which the
front hall (Valiyampalam) is used for special sacrificial
activities. The Madhyahara represents the position of
dipamala (Vilakkumatam), the trellis construction
carrying rows of lamps in nine or eleven rows. The
position of the Balikallu (altar stone) is in the region
of B!hyahara. The dhwajastamba is also located in this
region. The maryada is to be constructed accordingly
with g6puras on four sides.
In
included
Kathakali
large
for the
etc.
temple complexes NatyamaQqapam is
performance of dance (Natyam) , Kuthu,
In Kerala NatyamaQQapam is known as
Kuthampalam,
rectangular,
Fig.2{d). Their shapes are of square,
circle, elliptical and triangular. The
square or rectangular shapes are preferred in Kerala.
It is to be noted that the foundation of the incompleted
45(a)
NATYAMANDAPAM (KUTHAMPALAM)
f
0 0 a Cl 0 g Cl
[j 0 0 0 0 tJ 0 D
• • • • • • 2
(I 0
I 0 5
• 0
• 0 0 0
6 I(
s 0 c 0 0 0 0 Cl d , ,
Fig.2(d)
l. Rangarn
2. Nilavilakku
3. Mizhavu
4. Aniyara (Makeup room)
5. Hall (sabha)
6. Pillars
7. Entrance
46
KiIthampalam in Chengannur temple is of ell ipt ica1 shape.
2.12. TALAIIINA
This is a proportionate scale based on t~la which
is used in sculpture. The appropriate height of an idol
(bimba) is divided into 10, 9, 8 etc, equal parts. Then
each part is known as a t~la. When one ta1a is divided
into 12 parts, each part is known as angula. The measure
of 2 angula is a I kala I or I gOlaka' • Depending on the
number of divisions, the bimbas (images) are named
Da~ata1a, Navatala, AstatlUa etc. • In Navat~la system
the length of the face of the idol is fixed as one tSla.
*******
Chapter III
~BE CONCEPT OF • - VARIOUS APPROXIMATIONS
3.1. INTRODUCTION
The rat io of the cl rcumf erence of a circle to its
diameter, has fascinated mathematicians through the
centuries and the realisation that this ratio remains
the same for all circles is a great event in the history
of mathemat ics. It was Will iam Jones (l 706) who first
used the notation ( Pi) , a Greek letter, for
representing the ratio of the circumference of a circle
to its diameter and gained popularity by the adoption
of the symbol by one of the greatest mathematicians
Leonard Euler (1707-83) (12) . In 176"1 Lambert proved that
is irrational and C.L.F. Lindemtlnn, a German
mathematician, in 1882, established that is a
transcendental number which cannot be expressed as a root
of an algebraic equation with rational coefficients.
Various approximations to are implied or
explicitly stated in texts on V~stusastra, Sulbasutras
and in most of the mathematical works of Indian
mathematicians ranging from Aryabhata I to Ramanujan.
NIlakar;tt.~a even stressed the irrationality of 'V in his
48
'BhaI?Y~' on Aryabhatiya and Madhava{75) expressed ~ as an
infinite series. Many approx i mati ons to ~ are impl ied
in text s on t rad it iona 1 arch i t ectu re of Keral a such as
'Tantrasamuccaya' of Cennas Narayanan Namboothirippad,
'Thaccusastram Bha~a' (Gadyam) (author un known) ,
'KuzhikJditu Pacca' (47) of Mah~swaran Bhattathirippad etc,
in the construction of temples and altars. In this
chapter we deal wi th the approx ima te va lues of ~ wh i ch
are given in the available architectural texts.
3.2. VALUE OF • IN THE CONSTRUCTION OF V,TTAPRASADA
A method of construction of VFttaprClsada is
explained in (11; )
Tantrasamuccaya - . Since the prasada
(Srikovil) is having a circular plan-shape, a circle of
the desired circumference is to be constructed. The
method is described in the verse given below:
swabhr~tamane dasayuktasaptasatam~it~
viswalasacchatam~a:
yastena manena paribramayya vFttatmakam v~sma samatan~tu.
(Tantrasamuccaya, patalam 2, sloka 65)
This means that divide the desired perimeter of the
circle in to 710 parts and then draw a c ircl e wi th rad ius
49
equal to the measu re of 113 parts. This will be the
circle whose circumference is equal to the perimeter of
the VFttapr~s~da.
Let C be the e i reumferenee of the c ire! e. Then
accord ing to the above verse, the rad ius of the c i re1e
is C
710 x 113 and therefore its diameter is C
710 x 226.
But ~d :::; C
. C . . ~ d
C . 226C :::; T 7IO
710 :::;
226
355 :::;
113
:::; 3.1415929, approximately
or ~ ;;;; 3.1416, correct to four places of decimals. This
approximate value of ~ is implied in ~ryabhatiya of
~ryabhata I (A.D.499) as giv~n below:
Caturadhikam ~atama~tagu~am
dv§da9thistatha sahasr~nam
ayutadvaya vi9kambhasy~-
sann~ vrttapari~aha: (Aryabhatiyam, GaQitapadam, s16ka 10)
50
The rule reads "The circumference of a circle of diameter
20000 is close (asanna) to 62832". This implies the fine
approximation
~ = 62832/20000
= 3.1416
Thus the value of ~ a~sumed in the construction of
Vrttapr~s~da is more accurate than the Aryabhatian value.
3.3. VALUE OF • IMPLIED IN THE CONSTRUCTION OF GAJAr~~rHA
SHAPE
Another value of ~ is implied 1n the construction
of Gajapr~t;:ha (apsidal) type of temples. The plan shape
is a combination of a square and a semicircle. The
measurements of the sides of the Gajaprl}t;:ha shape are
given in the verse below:
sw~bhI~t~ pariuaham~nanicaye dh~mnaBca tu~~a~tibha-
gon~t~tadaBadha krteJrQQavamitairamBai: prthakkalpay~d
p~rswadvandva sam~yati mukhatatim ca, dvyamta sutrabhramat
praya: s~mghrira8amsan~hamapi p~?~ham hasti p!="?~hatmana:
(Tantrasamuccayam, patalam 2, sloka 67)
The rule states
gajapr~thaprasada
that
is to
51
the desired perimeter of the
be divided into 64 equal
d i v is ions and delete one d i v is j on from it. The remain ing
length is further div ided into 18 equal parts. Then the
front and the two sides are to be constructed with the
measu re of 4 parts each. The fourth side (rear side)
is completed by drawing a semicircle with the fourth side
of the square as d iamet er. Then the per imeter of the
semicircle will be approximately (pr~ya:) equal to the
measure of 6~ parts.
Let the perimeter of the pras~da be 64 units. When
it is divided into 64 divisions the length of each
division will be 1 unit. After deleting one division,
the remaining length of 63 d i v is ions is again d i v ided
into 18 equal parts. Then the length of each part will
be 3\ units. According to the above rule the length of
front and lateral sides of the prasada are of 4 parts
each. The rear side (ppHha bh§ga) is in the shape of
a semicircle whose Cl iameter is equal to the length of
the side, 4 parts. Ther.efore its radius will be of 2
parts wh ich is equal to 7 un its and hen ce the per imeter
of the semicircle is 7Q. But it is given that the
perimeter of the semicircular portion is approximately
(praya:) equal to 6~ parts which is equal to 21.875 units
approximately.
52
Perimeter of the semicircle:: 21.875 units, approximately
ie, 7'" :: 21.875 units, approximately
21.875 7 I approximately.
:: 3.125, approximately.
But the desired perimetf>r of the prasada is taken
as 64 units. The length of the front and lateral sides
equal to 42 units. Therefore the remaining perimeter
is 22 units. Hence the perimeter of the semicircle lies
between 21.875 units and 22 units. Thus the value of
lIT lies between 3.125 and 22/7. Further, the above rule
gives an important idea regarding the nature of the
number represented by "'. The radius of the semicircle
is stated to be 2 parts or 7 units whereas the
semiperimeter 7 lIT is defined as approximate (praya:) .
This implies that the value of lIT is only approximate or
it is not a rational number.
The above value of 11 have been found implied in
the M~nava Sulba Satra where the value of 1T is 1
approx ima tea to 25/8 or 3-8 . This value 1T = 3.125,
approx imately, also implied in the data found in ancient
Babylonian tablet (22) • Chih of China is said to have used
it in third century A.D. This value of 11 is used in
tradi tional architecture of Kerala for practical
purposes.
53
3.4. VALUE OF • IN THB CONSTRUCTION OF A CIRCLE WITH
PERIMETER EQUAL TO THAT OF A SQUARE
According to the rule of construction
(construction and rule is given in chapter VI) of circle
given in 'Tantrasamuccaya', the radius of the circle is
defined as a a 2 + 8' where a is the side of the square.
the perimeter of the circle = 2~(~ + ~) 2 8
5~a -;r-
If this perimeter is equal to the
5~a 4 -4- .- x a the square then
5~ = 16
16 ~ = 5
3.2
perimeter of
This value is greater than the other values of 11" given
in the above two cases. This approximation may be seen
in some of the eat"lier works on mathematics.
Bhaskara I(22) (early 7th century A.D.) has given the
approx imat ion,
54
Sin 61 = 41)(180 -M 40500 - -~-:-( 1'-8~O---$~)
Where is in degrees. For the radian measure of the
argument, we shall have
Sin ~ = Hi 1>(11 - cp) 511· - 4 ~(1f - cp)
For very small angles, we have
Sin cp = (l6/51f)CP
When q tends to zero and using that the limit of
Sin CP/CP is unity, we get the approximation of
16/5 == 3.2
This value of ~ is found implied in the Manava Sulba
Sntra and in the medieval Tamil work Kanakkadikaram of
Kari (after 12th century A.D.).
Another method is explained in 'Tantrasamuccaya'
and Kuzhikk~ttu Pacca and accor-ding to this method the
radius of the circle is determined as
r (1 + fi)a
4
where a is the length of the side of the square. (The
rule and method of con st ru ct i on is explained in
chapter VI).
55
Then the perimeter of the circle (circumference) will
be
2~(l + J2)a 4
= 11(1 -+- l2)a 2
When a = 4, the circumference of the circle is equal to
211(1 + /2) and that of the square will be 16.
If they are equal then,
211(1 + /2) 16
16 8 =
1 +72
= 3.314, approximately.
This implied value of 11 differ much from the approximate
value of 11.
3.5. APPROXIMATION TO , IN 'THACCUSASTRAM BHA~A'
'Thaccusastram Bhd~a' (gadyam) (5) is a book on
tradi tional archi tecture of Kerala, whose content is
similar to that of the 'Silparatna'. It deals with the
56
calcu lat ions and dimensions related to the temple
construction. A method of construction of a circle is
given at the end of the book. It is explained in the
lines given below:
'Vrttaprasadattinte cuttinekkondu ezhupattionnu
kurit~al atilorukuru kondu pattu karit~atil munnu kuru
ezhupattionnittatileppatinonnum kutakku~iya nilamulloru
kaiyurikondu vIcump61 vrttattinte suk~mam varum'(S).
The rule states "The perimeter of the Vrttapra'sada
(circular srlkovil) is divided into 71 divisions. The
length of one division is again subdivided into 10 parts.
Add the length of 3 parts to the length of 11 divisions.
The required circle is got by drawing the circle with
the above length as radius.
Let the perimeter of the Vrttaprasada be 71 units.
Then by the above rule the radius of the circle is equal
3 to 11 +10 = 11. 3 un its. . the perimeter (circumference)
of the circle = 22.6~. But it is assumed to be 71 units.
22.6 ~ 71
71 22.6
57
3.1415929, approximately
= 3.1416, correct to 4 places decimals
This is the same value of ~ impl ied in .&:ryabhat iya and
Tantrasamuccaya.
3.6. APPROXIMATION TO • IN FINDING THE RADIUS OF A CIRCLE
A method of finding the radius of a circle whose
circumference is known is given in 'Balaramam', a book
on traditional architecture of
is given below:
'Kupaparivrtalarddhflm
arddhake vim~ati dvayam
sapt3m~akam prabhGrikku
nTlamkolluka buddhiman ' .
(34) Kerala
The method
(Bal~ramam, Vrttapramaoam, page 39)
ie, the radius of the circle will be the length of 7
divisions when the semiperimpter is divided into 22
divisions.
58
If C is the c i rCl1mference and r represents the
radius then
r = C
2 x 22 x 7 --------(1)
But the circumference of the circle = 2~r
C
C ~
=
=
2~r
r
From (1) and (2) we have,
7C 2x22
7 72 =
C 2~
--------(2)
22 Thus the value of ~ assumed in this rule is
7
Chapter IV
THE GOLDEN RATIO IN TRADITIONAL ARCHITECTURE
4.1. INTRODUCTION
The Golden Ratio (or Golden section) which is
known as tKanakamuri t in traditional architecture is an
important concept
and arch i tectu ra1
in both
design.
ancient
It
and modern artistic
is the geomet r i cal
proportion in which a line AB is divided into two parts
by an interior point P in such a way that AB/AP = AP/PB
(ef Fig.4(a)].
P t
A B
Fig.4(a)
A rectangle
is called
whose length is in this
breadth a golden rectang le. In
we illustrate the existence of golden
ratio to its
this chapter
ratio in
traditional architecture, relation between golden ratio
and arddhadhika, and its application in the constructions
of NatyamaOQapa (Kuthampalam) and idols of deities
. (bimb~ .
60
4.2. THE CONCEPT 'GOLDEN RATIO'
Dividing a segment into two parts in mean and
extreme proportion, so that the smaller part is to the
larger part as the larger is to the entire segment,
yields the socalled Golden section and the ratio IS + 1
= 2
1.618 (approximately) designated as ~, is known as the
golden number. The ratl'o J? - 1 0 618 r x' atel 2 ., app 0 lm y I
is the reciprocal of ~. This number has many fascinating
qual it ies and the anc i ent Greeks cons idered the regu lar
pentagon which includes a number of 'golden ratio'
relat ionships, as a holy symbol. In a regular pentagon
PQRST there is a g olden rat io rela t ionsh i p between any
diagonal and any side of it, namely,
PR:PQ = 1.618 .•...
Further, all the diagonals intersect each other
in golden ratio such that, [.cf Fig.4(b)],
S
LR MR
T
= ~, MR = LM
Fig.4(b)
~, when ~ = 1.618, approximately.
61
In a regular decagon (10 sided polygon) the ratio
of a side to the radius of the circumcircle is also ~.
4.3. GOLDEN RECTANGLE AND ITS PROPERTY
A rectangle in which the ratio of the length to
width is equa 1 to 1. 618 approx i matel y, is ca 11 ed a golden
re c tan g 1 e [ c f Fig. 4 ( c ) 1 • Th is number ~ produces a set
of nesting rectangles.
PQRS is rectangle such that PQ
== ~, and PTUS a QR
is such that QR
~. a square --TO
S U R
2
1
5 6
3
4
T Q Fig.4(c)
62
This is a representation of the so called 'golden
rectangle' . If the 1 arg est square in a golden rec tang 1 e
is cu t away, the f igu re remain ing wi 11 also be a golden
rectangle. Such rectangles are characterised by a length
to width ratio of (1 + /S}/2, the golden ratio(4). It
is believed that the ancient Egyptians may have used this
ratio in the construction of Pyramids. This ratio recurs
often in number theory; for example
lim n~OO
Fn±l Fn
= 1 + Is
2
= 1.618 approximately,
where Fn is the nth Fibinacci number(4).
irrational number which is the solution of the equation
o.
Solving the above equation we have,
1 ± 15 x = -----
2
This is an
The golden rectangle whose sides are in the ratio
l:~ has the following property that the ratio of the
length of the smaller side to the greater side is equal
63
to the ratio of the length of the greater side to the
sum of the lengths of the two sides(49)
ie, 1
= ~
or is the mean proportion
between 1 and ~ + 1.
ie, 1 + ~ =
ie, ~2 _ ~ _ 1 o
If we divide the golden rectangle into two parts
such that one of the smaller. resulting rectangles is a
square then it follows that the proportion of the second
re eta n g 1 e i s 1: ~ its elf {c f (;'.1 q • t1 ( d) ] .
---~
1
/
('-<; ___ . 1 ~~-,--_l_~~
The proportion is
Fig.4(d)
<P - 1 and 1
get ~ • ~-- But ~2 - q> = 1.
multiplying by we
~ -- } ~ 'f which is the same as the original
proportion.
64
4.4. GOLDEN RECTANGLES AND FlBONACCI NU"BERS
A sequence of numbers each of which, after the
second, is the sum of the two preced ing numbers is known
as Fibonacci numbers. The sequence I, 1, 2, 3, 5, 8,
13, is a F ibonacc i soquence of numbers. This
sequence was discovered by Leonardo Fibonacci, also
known as Leonardo of P isa (1170-1250). The formula for
generating the sequence is
x = n
x 1 + X ~,where n- n-.-;
term of the sequence, n) 2.
x n
is the
Another formula for generating the Fibonacci
numbers is attributed to Lucas(4). It is given as
x = n
Further, the sequence of numbers(49),
I, 1.618, 2.618, 4.236, 6.854, 11.090,
(correct to three places of decimals only) have the
property that if we add the first two terms together
(l + 1.618) we get the third, 2.618. In the same way
the sum of the second and third 1.618 + 2.618 gives the
65
fourth, 4.236; and so on. Thus each sllccessive term is
the sum of the preceding two. Therefore it is a
Fibonacci sequence of numbers. In the above sequence
the ratio of any term to its preceding term is 1.618
which is the golden ratio.
The Fibonacci numbers can be used to make a golden
rectangle. Cons ider a un it square represent ing the first
term of F ibonacc i sequence. Then add a second square.
Add a third square to fit the longest side. Again add
a fourth square with its side as the longest side of the
above square. If we continue the process we will
eventually get a golden rectangle [cf Fig.4(e)].
Thus the
1 ~
1
Fig.4(e)
Fibonacci
rectangle are closely related.
3
- 2
numbers and the golden
66
4.5. GOLDEN RATIO AND ARDDHADHIKA
In Vastusastras, four types of width to length
ratios are defined in determining the width of the house
in gUl')am~a method. They are Samatata, padCidhika,
Arddhadhika, and PadOna (explained in Chapter I). They
define four categories of ratios of width to length in
rectangular buildings. The arddhadhika ratios are(58)
1:1.5, 1:2.5, 1:3.5, 1:4.5, 1:5.5, 1:6.5. I t is to be
noted that the ratios from 1:1.5 upto 1:1.75 are also
considered as arddha:dhika. According to
Manu~y~layacandrika (54), pad~dhika ratios are most suitable for
domestic buildings and arddh~dllika ratios are accepted
for buildings, idols, n~tyamat;lQapa etc, which have
aesthet ic values. Thus the golden ratio belongs to the
arddhCldhika ratios in traditional architecture. The
existence of golden ratio in traditional architecture
may be understood from the const ruct ion of KG. thampalam
of Kerala.
4.6. GOLDEN RATIO AND NATYAMA,DAPAM (KUTHAMPALAM)
'Tantrasamuccaya' (Silpabhagam) (16) of Kanippayyur
Damodaran Namboothirippad, gives a special method of
const ruct ing a Natyamal,.1Qapam (Kuthampalam) in temple
complexes of Kerala.
verse given below:
67
The method is explained in the
paryante pratiyonibhaji b~hirlltth~ v6ttarasya thava
maddhyasthe dalite, tat6 vibhajite samyak caturvvarggakai:
syadamsa: pada, m~yatistu vitaterdwa.bhyam padabhyam yutam,
tacchi~ta tati, ruttaram natanadhamnam dwitrisamkhyam matam
(Tan t rasamuccaya UH 1 pabh agam), Chapter 10, sI (jka 1)
This states that the pet:" Imeter along the uttara (beam)
of the natyamar;l<~apa must be of the 'pratiy6ni' (opposite
yoni) of that of the prasada (Srikov il) . [This is due
to the fact that the na tyamandapam and the Sr ikov i 1 are
facing each other]. This perimeter may be measured
either along the central line or along the boundary line
of the uttara (beam). Divide the semiperimeter into 16
equal parts and each part is called a 'pada'. The length
of the maOQapa (along uttara) is obtained by adding 2
pada to the half of the semiperimeter (to % of the
perimeter) and the width is determined by subtracting
this length from the semiperimeter.
Let us examine the ratio of the length to width
in the above construction of rectangular NAtyamaoQapa.
68
Let the perimeter of a Natyamal')Qapa be P and a be the
side of a square of the same perimeter.
Then P
Semiperimeter
Dividing by 16, we get, P 32
==
:::
4a
P 2"
== 2a
== This is the unit
'Pada' defined in the text. .". by the above verse we
have,
Length of the Natyamandap,lm a 2 ::: a + x
8
a ::: a + 4
5a :::
4
Width of the Mandapa a
2 :: a - x 8
a _ .. a - -4
3a :::
4
3a Width 4 = Sit Length
4
3 == S-
ie, Width:Length ::: 3:5
or L:W
69
=
5:3
5 3
= 1 . 66 .....•.
But the golden ratio is 1.618 (approximately).
the above ratio is very close to the golden ratio.
4.7. CONSTRUCTION OF BIMBA (IDOl.) AND GOLDEN RATIO
Hence
It is significant to note that the bodies of many
living beings (natural organisms) including man (the
human body) , are really based on golden ratio
relationship. For exampl e, the rat io of the he ight of
the navel from the feet to the height of the head from
the navel (of a man of standard height) is ~. In the
construction of Navatala or Da~atala bimba (idol), the
ratio accepted in Tantrasamuccaya(lS) is 1.6, approximatel~
which is very close to ~.
In the case of Nava tala bimba, the total height
of the bimba (idol) is divided into 108 equal parts and
each part is called an angula. Two angula form a 'Kala'
or 'Golaka ' and 12 angula conRtitute a 'Tala'. Since
70
the height of the bimba is 9 Tala, it is known as
N.iwatala bimba. The height of the idol is divided into
two parts at the navel point in such a way that 66
angulas are below the navel point and 42 angulas are
above it. Then the ratio of these lengths is equal to
66 42 = 1.6, approximately, which is very close to the
golden rat io. Further, the ratio of the total length
to the height of the bimba upto the navel is
108 66
= 1.6363, approximately.
This is also very close to the golden ratio and belongs
to the arddhadhika.
Similarly, in the case of Dasatala bimba, the
total number of divisions is 120. The ratio of the
height of the navel from the feet to the height of the
head from the navel is 73/47. The value of the ratio
is approx imately equal to 1.6 and the rat io of the total
height to the height of the navel from the feet is 1.64,
approximately. Thus these two rat i os are very close to
the golden ratio and they belong to the arddhadhika.
71
Thus the golden ratio which is a special case of
arddh§dhika ratios is used for constructing artefacts
having aesthetic values, in the traditional architecture
of Kerala.
*********
Chapter V
TRAIRA~IKA (THE RULE OF THREE) IN TRADITIONAL ARCHITECTURE
5.1. INTRODUCTION
The traira~ika or direct proportion was used as
an effective tool in solving problems of Astronomy,
Ari thmet i c, Geomet ry and Arch i tecture. Th is
be traced in BCikh0)3h:Il i Manuscr i pt (32) (abou t
method may
1 st century
A.D.), Aryabhatiya (A.D. 499) and in all other works on
mathematics. According to Bhaskara 11 (A.D. 1511), the
Rule of Three is the essence of arithmetic(17) and it
pervades the whole of the science and calculation. The
Rule of Three is largely appreciated because of its
simplicity and its universal application to ordinary
problems.
In this chapter we explain the application of
trairatdka in determining the length of the side of an
octagon, sixteen sided polygon etc, and in making the
holes for collarpins (vala) on rafters.
in calculating the lengths of .ra fters.
It is also used
73
5.2. DEFINITION OF TRAIRASIKA
Trairasika is defined in Yuktibha9a (66)
lines given below:
"tray6 ra~aya: sam~hrt§: karaQam yasya,
sar~si: k~rye karaQopacar~l
trir~sirbhavati, sapray~janam
yasya tal ganitam traidisikam"
as in the
(Yuktibhd9a, Chapter 4, page 45)
Here three quantities are needed in the statement and
computation. So this rule is known as Trair~sika (The
Rule of Three terms). If four quantities are in
proport ion,
knowing the
there are
then anyone of them may be determined by
values of other three quantities. Since
three known quantities, it is called
Trairatika. Similarly, there are Pancarasika,
Saptara.s ika, Navarasi ka et c, depend ing on the number of
known quantities used for calculating the unknown. In
traira~ika, the method of calculating the unknown is
given in lines below:
74
Iccham phal~na samhatya pram~Qena vibhajayel
Icchaphalam bhav~l labdhamevam trair~~ikam matam!!
(Yuktibh~~a, Chapter 4, Page 46)
ie, Icchaphalam is got by d i v id ing the produ ct of I ccha
and PramaQaphalam by Pramaoam.
ie, Icchi3phalam = Iccha x Pramaoaphalam PramaJ;lam
where Icch.§. the desired antecedant,
a proportion
term in
Icchaphalam the desired consequent / the fourth
proportion
Pramanam the antecedant, the first term of
proportion
Pramanaphalam: the consequent, the second term in a
proportion
The above relation may be expressed as
PramaJ;laphalam PramaQam
= Icchaphalam Iceh.§.
a
The pramaQam and Iccha must be of the same denomination.
75
If x and y are the magn i tude of two quan tit ies of the
same kind measured in thp ."lamp. un i ts, the ratio x: y or
x/y may be used to compare the magn i tudes. It gives the
number of times y is contained in x. Here the number
of times of pram~Qa in pramaQaphalam will be equal to
the number of times of Icch~ in Icch~phalam. If the
Iccha becomes larger than Pram~l')am then Icchaphalam
becomes larger than pram~~aphalam and vice versa.
5.3. VYASTA-TRAIRASIKA
The inverse proportion (Inverse Rule of Three)
is called Vyasta-trair~1:!ika. According to Sridhara, the
method is to multiply the middle term by the first and
to divide by the last, in case the proportion is different
(inverse) (17).
The inverse proportion is defined in lines below:
"Iccha vrddhauphalahr!sa Icch~hras~dhikam phalam!
Yatra tatra hikarttavyam Vyastatrairasikam budhai:!!
(YUktibh~~a(66), Chapter 4, Page 48.}
ie, when the Iccha increases than pramal)am, the
Icchaphalam decreases than thp. pram~Qaphalam and vice
76
versa. This rule is known as Vyastatrairallika (Inverse
proportion). The computation is explained as
"Vyastatraira~ikaphalamicch~ bhakta: pram~oaphala gh~ta:!"
ie, Icch~phalam =
or this may be expressed as,
Iccha Pramar,lam
Pramanam x Pramanaphalam Iccha
Pramanaphalam Icchaphalam
5.4. METHOD OF FINDING THE INCLINATION OF THE COLLARPIN
ON AN INCLINED RAFTElt
Consider the rafters (lupas), collarpin (vala),
Eaves-reaper (V~mata) on the roof of a square maoQapa.
The collarpin (vala) will be perpendicular to the sides
of straight rafters and therefore the holes on them for
collarpins will be perpendicular to the sides so that
the 1 ength of the hole is equal to the th i ckness of the
rafter. But in the case of inclined rafters, the
collarpin is not perpendicular to the rafters and
correspondingly the holes on them are inclined at an
77
angle which may be determined as in the method given
below using traira§ika. [cf Figs.5(a) and 5(b)].
o
A B c
Fig.5(a) Fig.5(b)
Let 0 be the pos i ti on 0 E the Kootam on wh ich an
end of each rafter is fixed and OA, OB, OC represent the
positions of rafters. Let ~B~ represents the
eaves-reaper at the lower end of the rafters and t, B' e' be the collarpin (vala).
A---rt' 11 AB and A--rt' 1 Cf'A, the straight rafter.
Let.t be the ang le between 6A and OC, the incl ined rafter.
Then the incl ination of the hole on 6C will be
78
proportional to the angle: [Fig.5(b)], gives an
enlargement of the rafter and the angle~ on it.
From the figures above,
A OAC and ~PQR are similar, by the rules of
similarity of two right angled triangles given in
Yuktibha:;;a (66) •
The first rule states that the two triangles
(right angled) will be similar if there is "parallelism
between the hypotenuses and aside of each". This rule
may be proved as below.
6 OAC and 4PQR are r.ight angled triangles.
PR " A-C
~ 11 QC
Le == I.B
Further, M.C ::: \QEE and
~ ::: (Q
= 90°
79
Therefore the two triangles are equiangular and
by AAA-theorem, the above two triangles are similar.
Since the triangles are similar, by Rule of Three,
we have
where,
Icchak~etrabhui~ PramaQak$etrabhuja
Pramanakl?etra
bhuja
k6ti
karQam
ie, QR AC
QR
=
=
=
:::
Icchd'kgetrakoti Pramanak~etrakoti
Icchak$etra Karoam Pramanak~etra KarQam
desired region
given region
base of the triangle
attitude
hypotenuse
PQ OA
PH QC
PQ x AC OA
80
PO is the thickness of the in cl ined rafter, OA is the
length of the straight rafter and AC is the distance of
the incl ined rafter from the Rtraight rafter. lQ!'R is
the angle of inclination of the hole for collarpin. Thus
the incl inat ion of the call a rpin to the side of the
inclined rafter is determined by OR.
Note: It is to be noted that in traditional architecture
the slope is not expressed
example, the pi tch of a roof
in terms of degrees. For
is not expressed in degrees
bu tar a t i 0 0 fir i s e I and I run I ( V er tic alp r 0 j e c t ion and
horizontal projection). Usually, the rise is expressed
as a certain number of angula per kol of run thus, a
rise of 6 angula means that the roof rises 6 angula for
each 24 angula that it runs horizontally. Here the pitch
is 6 to 24. In the above resul t OR is known as the
length of the inclination of the hole on the rafter.
5.5. DETERMINATION OF HEIGHTS OF THE ROOF FOR DIFFERENT
PITCHES
The idea of Trair~sika is made use of in the
calculation of the pitch of the roof. Consider a
gabled(18) roof of a building which is a 3-dimensional
81
space-fr-ame. The er-OBe Rect.ion of the roof will be in
the for-m of an isosceles tr.ianqle whose base is the width
of the house and the sides ar-e the r-afters on either
sides of the roof. The altitude of this triangle which
is the he igh t of the r-oof fr-om the 1 evel of the
wallplate, divides the tr-iangle into two right-angled
triangles. In gener-al, the normal height of the r-oof
was taken to be equa 1 t r) the sem i -widt h of the house
so that the angle of incl inat ion of the r-oof with the
horizontal was 45°. But cer-tain variations in heights
of the roof were adopted depending on the aesthetic
considerations and the materials used for covering the
roof.
In t radi t ional arch i tecture the decrease in height
from the normal height was defined as
expressed as a
the semiwidth
'aviccil' or
'amippu' (dip) . It was ratio of the
of the house. height to unit length of
Multiplying
we get the
this method,
base (l kol)
correspond ing
Trair~sika •
this ratio by the corresponding semiwidth
height of the roof for that 'aviccil'. In
an elemental rightangled triangle of unit
was cons idered for each av ice i 1. The height
to each width were calculated using
The principle behind this· is given by GaniHsa
82
(1545) (17) as "if the upright, base and hypotenuse of a
rational rightangled triangle be mUltiplied by any
arbitrary rational number there will be produced another
rightangled triangle with rational sides". It is implied
that when the sides of a right triangle are increased
proportionally, the rat io of the height to base remains
the same ie, the slope of the roof wi 11 be the same for
the same aviccil (dip).
In traditional system the height is said to be
24 angula if the roof rises 24 angula for each 24 angula
of semiwidth, and the aviccil is expressed as 24/24,
called 'thankurmam' (71) • The av iccil is named as 1/4
angula, 1/2 angula, 3/4 angula etc, corresponding to the
ratios 22~/24, 21/24, lY~/24 etc. In each case the
height is diminished by l~ angula and each can be
expressed in non-recurring decimals.
In a similar way corresponding to each aviccil,
the lengths of the rafters may be determined using
traira~ika, by knowing the length of the hypotenuse of
the elemental right angled triangle with unit base (1
kol) . The accurate 1 ength of the common rafter is got
by multiplying the length of the hypotenuse by the
83
semiwidth of the bu i Id ing and add ing hal f the width of
the rafter to it.
5.6. 80ME OTHER PROPORTIONS OF HEIGHT AND WIDTH
The height of the ridge from the level of
wall pIa te depends on the w id th of house. Th is is ev ident
from the following lines in Vastuvidya(13).
Uttarasyanurap~~a
tasam taramudlritam
(Vastuvidya, Chapter 10, Verse 1.)
ie, the height is prnpor-t iona I to the semiwidth of the
house. The proportions of height to semiwidth are
defined as 1:1,7:8,6:7,5:6,4:5,3:4,2:3 and 1:2 [ef
Fig.5 ( e) ] • These proportions are named as Ambaram,
Viyat, Jyot is, Gaganam, Vih~yas,
and Puskalam respeetively(33) . . Anantam, Antarik~am,
l~ 7~6~ 5~ 1 8 7 6
4~ 5
l~ 4 3 2
Fig.5 (c)
84
Manu~yalayacandrika stirulates the height of the
ridge equal to the semiwidth of the building. In this
case the incl ination of the roof will be 45 0 • The
proportion 2:3 is accepted for practical purposes in
later construction <)f buildings where the inclination
of the roof is about 33~o.
5.7. DETERMINATION OF THE LENGTH OF THE SIDE OF AN OCTAGON
A given square may be transformed into an Octagon,
Six teen sided polygon, Thi r ty two sided pol ygon etc, and
finally to a circle by the successive division of the
sides of the squa re and del et ing the t r i ang I es at the
corners.
determining
(66) polygons •
The principle of trair~§ika is applied in
the length of sides of the regular
Consider a square ABCD of side a. Let the two
lines through the midpoints of the sides intersect at
o forming 4 small sqUAres 1n the given square [cf
Fig.5 (d) ] •
85
D~ ____________ ~~~~ ____ ~C
B "'ig •. IJ(d)
Join 0 and C. Let PQ meets 6c at R and OS = OP
60PC is an isosceles triangle. ~ 1 QC and TS 1 oc
CR PramiQam
CP PramaJ)aphalam
OC - os
Iccaphalam
cs
Icca
eT
CP x cs CR
OQ.
86
Mark points on each side of the square at a distance of
eT from each corner. ie, eT = CU. Delete 4 triangles
at the corners each equal to ~CTU to form the required
octagon. TU will be n side of the octagon = a-2CT. Let
s' be a point on 6T such that OP .., OS'.
Draw aline WV J 6~1 through S'. Then using
trairasika as above we 'let,
TV TS x TS', where SL lOT. TL
Delete triangles at the corners of the octagon each equal
to A TVW to form a regu lar l(3-,8 ided polygon. Continueing
this process, we wi 11 reach a pos i t i on when the polygon
approximately becomes a circle. The idea of 1 imi t is
implied in this process.
5.8.1. DETERMINATION OF LENGTH OF RAFTERS USING TRAIRXSIKA
The idea of Traird~ika is used in determining the
lengths of rafters. In V~9tus~stras, there are many
methods def ined for find i nq t. hf' lengths of rafters. The
process may be different tn each method due to many facts
such as tradition, regional difference etc, but the
87
result will be the same. 'l'hp.se methods and rules are
evol ved through years of continuous practice and
evaluation. Tedious computational process was a
hindrance to the trnd i t iona 1 architects and so they
formu lated simple and PflSY methods for finding the
measurements of various plpments of building.
The traditionill architects of Kerala have
developed some practical methods for finding the lengths
of rafters. They defined suitable 'scales' (proportional
units) and named as Pram~nas . (Postulates) in terms of
the scales which are used for finding
of rafters. The Postulates (PramaQas)
Postulate (Ettam Pramat;lam) I
the
are
true lengths
known as 8 th
Postulate
) 6 th 1 ( - _.) (33) Prama':lam , Postu ate Ar~m Pramar;tam etc.
5.8.2. 8TH POSTULATE (ETTAM PRAMANAM) AND LENGTH OF RAFTERS
In this method the requirements are a wooden
board, an ax e and a measu ring rod. This wooden board
is named as measllrement board (Prama~appalaka).
Construct a right angLpcl t.rianqle OAB on this board in
such a way that the proportlonal.e scale is 1 kol (72 cm)
= 3 angula (9 cm) or 8 angula '" 1 angula (3 cm). 6A is
called the bhuja and OB is called the koti. [cf Fig.S(e)]
88
B
y
Bhuja Z 0r-----~~--------__ ~--~~ C
x
Fig.S(e)
Let x angula be the width of
A on the bhuja such that OA = ~ .
the house.
x 2 angula
A'
Mar-k a point
x = 16 x 3 cms.
Let y angula be the height of the r-oof suppor-t. Put a
mar-k at B on the koti such that OB = ~ x 3 cms. Let
z angula be the eaves pr-ojection (kazhukkol chat tarn) •
Mark another point C the bhu:ia such that 3
3 on AC = - x ems. 8
Draw a line parallel to koti through C. Join the points
B and A and produce it to meet the parallel through C
at A' • Then BA I is the l/sth of the length of the st.
rafter ie, 8BA' gives the length of straight rafter from
the ridge to the tip of the eavesprojection. 8BA
represent the length of the rafter from the ridge to the
89
notch on the wallpl~tp for fixing the rafter on it.
Since the scale is tak(~n as 8: I, this method is known
as 8 th Postulate in Kerala.
The advantage of this method is that the space
used for drawing the figure is diminished to l/sth of
the usual method. But calculations and figures are
different for different situ~tions. This problem is
th solved in the 4 Postulate (Nal~m Pra~ct~am).
5.8.3. 4 TH POSTULATE (NALAM PRAMANAM)
Here the requirement is a small rectangled wooden
board which is known as 'Mattappalaka' or simply
'Mattam'. This is used aA a key instr.ument for measuring
and marking several minute elements of a building [cf
Fig.5(f)] • -t - - -- - _ ... -. ----- - --, B
! 7.5 cm
O-----------lr~~------------~~
'- • - •••• L
Fig.5(f)
90
Consider a right angled triangle with base (bhuja)
4 angula (12 cm) a.nd altitude (koti) 2~ angulam (7.5 cm)
on this board. The length of the hypotenuse is defined
as the I scal e I or un i t of measu rement in this method.
The true length of the straight rafter (common rafter)
from ridge to the outer
taking 6 times of this
semiwidth of the house.
8dIJe 0 f the wallpla te is got by
, sCill e ' per 1 kol (72 cm) of the
For an illustration, let 2x kol be the .width of
the house and 1 be the 'scalp' (unit of measurement).
Then the length of the strAight rafter is 6xY. By giving
differen t values for x, w{~
of the rafters from the
height remains the same.
qet the correspond ing 1 engths
Hbove formula, provided the
One of the features of this
method is that the 'scale' used in this method is
independent of the width of the house and may be used
for all widths having the same height. Even though this
method is not given on any pages of Vastusc!stra texts,
this was used by the traditional architects and the idea
was transmitted from generation to generation through
teacher-student relationship and verbal teachings.
91
c
B
(7.5 an)
o .12 cm)
F'lg.'i(g)
By an extens ion of t his met hod, the 1 ength of the
hiprafter may be calculated. For this, consider the
diagonal of a square wi th side 4 angu la (12 cm) and mark
this length on the bhuja at D. Then BD will be the
'scale I for calculating the length of the hiprafter from
ridge to the outer edge of the wallplate [cf. Fig. 5 (g) J •
If we have to increase or d~crease the pi tch of
the raf ters I then the lengt h OB is to be increased or
decreased accord ing 1 y • Thus this was a universal method
formulated by the traditional ar.chitects of Kerala.
92
In all these methods t.he principle of trair~~ika
is applied. Further it is convenient to have the width
of the house in multiples or submultiples of pada (8
-angula) units.
**""*******
Chapter VI
GEOMETRICAL CONSTRUCTIONS AND RELATED MATHEMATICAL CONCEPTS
6.1. INTRODUCTION
The plan shape, determined
perimeter (paryanta sutra), is known
In the traditional architecture of
by a bounding
as the ma~Qala.
Kerala seven
geometrical shapes are definpd for ma9~ala which are
given in the following lines.
"Vrttam vFtt~yatamapy~yata ~aturam ca samacaturam
ezhunt~krti sadan~ sadastakon hastiprstha mennittham". . . - - ... (Balaramam, page 66)
The plan shapes are circl~, elongated circle, rectangle,
square, hexagon, octag on and gajap!="~tham (apsidal) .
Usually triangular shape 11'3 not accepted for buildings
of domestic purposes. Most C)f these shapes are used
in vedic period for constructing different types of
yajna-vedis and mantra-yantras.
In this chapter we illustrate the method of
construction of these shapes and their architectural
94
values implied in vastu'slistras. The constructions of
a triangle, rectangle, hexag on, octagon and circle each
of which having the same perimeter of a given square
and deduction of mathematical values assumed in them
are explained in detail. The geometrical method of
determining the lengths of rafters are also included
in this chapter.
6 • 2 • 1. SQUARB
The square is literally the fundamental form of
Indian architecture. The form of a Vastupuru~amar:t9ala
is a square. Earth is symbolically represented by
square and it is known as the Brahmamal')qala. The square
mal')gala has the highest efficiency of space enclosure
when compared to other quadrilaterals. It can be
converted into a circle, triangle, hexagon, octagon and
a rectang 1 e • The method of construction of a square
is given in Tantrasamuccaya (15) • A rectangle may be
obtained from a square by elongation (ayamam) and ~
regular polygons of 8 sides / 16 sides etc, are derived
from the square.
95
6.2.2. CONSTRUCTION OF A SQUARE
The method of construction is given below:
Pragagram sutramurvya mrjGtara mabhikalpyasya mGlagragabhyam
aGtrabhyam matsyayugmam yamasasiharit6: kalpayi tva trafsiltram
krtva dik~vankayitva samamiha vihitai ssGtra kai: kOQamatsyan
k;-tva f sphalyai~u sutram racayatu caturasram pura: kl?etraknuptau
(Tantras~muccaya, patalam 12, slokam 23)
To construct a square, draw a line segment in
the plane of the earth in the East-West direction wi th
the help of a rope (about 1 kol in length) [cf Fig.6(a)].
n' '6 C - ...... .r f'\ ..-\ / \
,/ 0
\
\ I \ . ~ \. !i' "-,
A ",'- B
Fig.6(a)
96
Then draw two circles with their centres at the
extremities of the 1 ine segment and radii equal to 3/4th
of the length of the 1 ine segment. The intersection
of the circles will be in the shape of a fish (fish like
line) and the 1 ine through the poin ts of intersect ion
of the circles will determine the North-South direction.
Draw four equal circles with their centres on four
directed line segments at a fixed distance from the
point of intersection of the two lines. Join the points
of intersection of the circles (tips of fish like lines)
to get the required square.
6.3. CONSTRUCTION OF A RECTANGLE WHOSE PER~METER EQUAL
TO THAT OF A SQUARE ( 58)
Consider a square of the given perimeter.
the square into 64 cells (pada) (8 x 8 gr ids) •
Divide
Delete
a row of cells along a pa i r of opposl te s ides of the
square. A column of equal square cells is adjoint to
the other two s ides of the squa re. Then the resulting
figure wi 11 be a rectang I e whose per imeter is equal to
that of the square and whose sides wi 11 be in the rat io
3:5 [ef Fig.6(b)].
97
0' C'
o c
A jj
A' B'
Fig.6(b)
ABeD is a square of 8 x 8 (pada) space module and
A'8'C'0' is a rectangle of to pada x 6 pada module. The
perimeter of the square is equal to 4 x 8 units and the
perimeter of the rectangle is (10 + 6)2 unit, ie. 32
units. Hence the perimeters are equal where as the
(areas are different. Th i s pr inciple is made use of in
,the construction of NatyamaQQapa.
98
6.4.1. CIRCLE
A circle may be def ined as the locus of a point
which moves such that its distance from a fixed point
always rema in s a
perfect shape in
constant. It was
Va~tuB~stra. In
considered the most
Tantrasamuccaya(15)
a method of drawing a circle is given (explained in
Chapter Ill) . Square and circle are coordinated in
architecture from the vedic period.
6.4.2. CONSTRUCTION 01' A CIRCLE WHOSE PERIMETER IS
EQUAL TO (APPROXIMATELY) THAT OF A GIVEN SQUARE
The method is given In thp following lines.
KarQQarddha sutrasya bhuj~rddhatoti
riktam~akarddham bahi rankayitva
madyastha sutram parivarttya kUQgam
kurvita ca~9adyuti ma~9alabham
( 15 ) (Tantrasamuccaya , patalam 12, sloka 29)
This rule states that take the half of the
difference between the semidiagonal and semiside of the
qiven square. Add this quantity to half the length of
99
the side. Then draw a circle with this length as radius
and centre at the centre of the square.
the required circle.
Fig.6(c)
This will give
Let a be the length of the side of a square ABCD.
Let the diagonals A-C and BD intersect at 0, which is
the centre of the square. Take a point P on Cl> such
that OP == a/2, hal f of the length of the side of the
square. Let Q be the midpoint of Pn. Draw a circle
with centre at 0 and rad ius equal to OQ. Then this wi 11
be the required circle whose perimeter is
(approximately) equal to that of the square [cf Fig.6(c)].
100
Since a is the length of the side of the square,
OD ha =
2
a + .!.( l2a ~) r = 2" -2 2 2
= ~ + ~(r2 - 1 ) 2 4
(1 + !2) a = 4
When a = 4, the perimeter of the square is 16 units and
the perimeter of the circle is 2~(1 + )2).
Another method is stated for circling the square
of the same per imeter. According to this method we have
to add a quarter of the half length of the side of the
square to the half length of the side, ie, add 1/8th
of the side length to half of the side length. This
will give the radius of the circle.
_a + a ie, radius of the circle is 2 8
perimeter of the circle = 2~(~ + ~) 2 8
101
If we take the value of 4IJ' as 3.14, the perimeter of the
circle, in the first case, will be
= 241J'r
2 x 3.14 x a(12 + 1) 4
where a is the side of the square.
When a = 4,
Perimeter, C = 2 x 3.14(/2 + 1)
= 15.16126 units
But the perimeter of the square is 16 units. Similarly
in the second case per imeter of the ci rcle is 15.7 when
, is 3.14.
Thus in both the cases the value of 4IJ' was assumed
to be greater than 3.14.
Further it may be seen that the perimeter of the
circle will be approximately equal to that of the square
if we take the radius of the circle as
r =
ie r =
=
~ + !!( [2 - 1) 2 3
3a + 2[2a - 2a 6
102
a(212 + 1) =
6
Perimeter, C = 21Tr
21T[a(2~ + 1) ]
When a = 4,
C = 41T(212 + 1) 3
If c = 16 units
= the perimeter of the square, then
16 x 3 1T = 4( 212 1 ) +
12 = 2/'J. 1 +
= 3.13445 (approximately),
which is very close to the value of 1T and the per imeter
is 16.000017, approximately equal to th~ perimeter of
the square.
6.5 .1. GAJAP~~1HA AND Y~TTAYATA
There are two shapes whi ch are un ique in Ind i an
architecture. They are (apsidal) and
'rttay!ta (elongated circle) or Ayatav!="tta shapes. The
103
The apsidal shape, resembling the rear side of an
elephant, is a combination of a square and a semic ircle.
The vrtt~yata shape consists of a square with two
semicircles at the ends. Generally these two shapes
are used for temple construction. The method and
measurements of constructing gajapr9~ha and vrttayata
maQQalas
Pacca (47) .
are .. (15) glven In Tantrasamuccaya
Vrttayata is sometimes called
and Kuzhikkat
by the name
Dirghavrtta. The method of construction of gajapF9tha
shape is explained in chapter Ill.
6.5.2. METHOD OF CONSTRUCTION OF DIRGHAV~TTA
(ELONGATED CIRCLE)
The method of construction of Di rghavrt ta
explained in the verse below:
bh~gadvay~ dviradapF9~ha samuktanitya
v~ttikrt~, tadubhayantarabhagadairghyam
sweddhmamsato virahit~na gUQ~msakena
is
vrttayat~ vitanuyat suravaryadhi~ftye
(Tantrasamuccaya(lS), patalam 2, sloka 68)
Constru ct sem i ci rcles at the front and rear side with
radius equal to 2 parts as described in the case of
104
Gajapr~tha shape. Then divide the length of 3 parts
into 21 divisions and delete one division from it. The
remaining length will be the length of the middle line
segment (lateral sides) join ing the two semi circles on
either sides [cf Fig.6(d)].
Divide the desired perimeter into 64 equal parts.
Then the semicircles are determined wi th diameter equal
to the length of 14 parts and the lateral sides of the
rectangular portion
defined by 10 parts.
C I I
I I I I
dl I
in between the semi ci rcles are
Fig.6(d)
After di v id ing the per imeter into 64 parts, delet e
one part from it. Then divide the remaining length into
18 divisions and length of each division will be 3~
105
parts (of the former division) .
• . radius of the semicircle = 2 divisions
= 7 parts
diameter = 14 parts
The length of the lateral side
= 3 divisions
3 d' .. - 12 IVISIOnS
= 10~
lO~ parts - 21 parts
= (lO!z - ~) parts
= la parts
Thus the perimeter of the elongated circle is equal to
the sum ·of the perimeters of two semicircles and two
lateral lengths of the rectangular portion.
ie, Perimeter = ~ x 14 + 2 x la parts
If the perimeter is 64 units, then
64 = 14 x 22 + 20 7
= 64 units which is true.
Here the value of ~ is implied to be 22/7.
106
6.5.3. DETERMINATION OF THE PERIMETER OF THE DfRGHAV~TTA
Let P be the perimeter of the elongated circle.
Then P = 2 x perimeter of the semicircle + 2 x length
of the lateral side of the rectangular portion
= 2 x ~r + 2 1, r, the radius of the semicircle
= ~d + 2 1, d, the diameter of the circle
and d = width between the lateral sides
From above,
the width= d
P 14 = 64 x
and d 14
= 1 10
1 d x 10
= 14
Perimeter,
P ~d 2 d
:: + 1.4
d(~ 1
= + 0.7)
107
When d = the diameter of the semicircle is known,
P may be calculated.
IfP = 64,
l4(~ 1
then P = + --) 0.7
64 ~
1 14
= + 0.7
64 1 ~
14 = .7
2.2 -:7 = ~
22 = 7"
When ~ = 22 7'
p = d{22 + ~) 7 .7
= 32 d 7
Thus the perimeter of the elongated circle is
determined when the width (max. width) of the
rectangular portion is known.
Note: In some texts it is seen that the length of the
rectangular portion is taken as the radius of
the semicircle.
108
6.6.1 • TRIANGLE
A triangle appears to be a mystic shape in tantric
rites and architectural ornamentations, but not much used
as grha-vastumaf)Qala. The inscription of triangles in
a 'Sricakram' is an example for this. Bharata Muni in
his 'NatyasCistra 1 describes triangle as a suitable shape
for the construction of 'Natyagrha' (Kuthampalam) .
Throughout history the commonest covering of the building
is the trussed roof, constructed upon a frame composed
of triangular sections spaced crosswise at intervals and
made rig id in length by beams. The truss is based on
the geometric principle that a triangle is the only
figure that cannot be changed in shape without a change
in the length of its sides. Thus a triangular frame of
strong pieces firmly fastened at the angles cannot be
deformed by its own load or by external forces such as
the pressure of strong wind or rain. This principle is
made use of in the construction of Malabar gable a
triangular projection at the top extremities of tiled
or thatched roofs. It is the characteristic feature of
Kerala style of architecture which is noted for its
!beauty and utilitarian simplicity.
\
\ The higher derivatives of triangles regular
109
polygons of 6 sides, 12 sides etc, were rarely used
except for ornamental works and temples.
6.6.2. CONSTRUCTION OF A TRIANGLE WHOSE PERIMETER IS
EQUAL TO THAT OF A GIVEN SQUARE
The method is described in the following lines.
sasthamsakam yamahimamsudiso: pratIcya . "
sotre suy~jya haridigbahirankayitva
t~naiva te~u suvidhaya ca sutrapatam
kuryattrikoQaparimaOQita vahnikuQqam
(Tantrasamuccaya, patalam 12, sloka 28)
Divide the length of the side of the square into
6 equal parts. Extend the western side of the square
by adding one part each to the Southern and Northern
ends. Put a mark on the exterior side of the square at
a distance of 1/6 th of the length of the side of the
square from the Eastern side. Draw 1 ines join ing th is
mark and the ends of the Western side. The resul ting
~triangle will be the required one.
110
Let ABeD be the given square with side a. Divide
the length a into 6 equal parts and add one part each
to either end of the side ~.
R
Fig.6{e)
Let PQ be the extended side and R be the point
at a distance of 1/6 th of AB from CD. Join PT{ and ~.
Then PQR is the required triangle [cf Fig.6{e)].
From Fig.,
AB = a cm
PQ =
III
4a =
3
a RS = a + -
6
7a == 6
PR 2 ::: (2a) 2 + (7a)2 3 6
4a 2 +
49a 2 == g- 36
== 65a 2
~
Perimeter of i\PQR 2165 a 4a
== + 3 6
/65 a + 4a :::
3
a (8.062 + 4) ;;;;; -
3
12.062 x a == 3
== 4.02 x a cm
When a == 6 cm, Perimeter == 4.02 x 6 = 24.12 cm.
But the per imeter of the square when a == 6 cm is 24 cm.
Hence the perimeter of the triangle 1S greater than that
of the square by .02 x a units.
112
6.7. CONSTRUCTION OF A HEXAGON WHOSE PERIMETER IS EQUAL
TO THAT OF A GIVBN SQUARE
This method is given in the verse below.
ankau prakalpya haripancamadikpadikthau
~a~~hamsat~ bahi rate nijamaddhyatasca
dvau dvau jha~au paradisorapi matsyacihna-
~atsGtrakairvviracaye drasakonakundam T (15) ..
(Tantrasamuccaya ,pata1am 12, s10ka 30)
Draw a line in the East-West direction through
the middle points of the side and take two points on this
line on either side at a distance of l/6 th of the length
of the side. Draw three equal circles with their centres
at the extremities of this central line segment and at
its mid point and radius equal to the semilength of this
line segment. Join the points of intersection of these
circles (two fish like lines) and the end points of the
line segment successively to form the required hexagon
[ef Fig. 6 ( f) ] •
Instead of taking the East-West line we can take
the South-North line and proceeding in the same method
we get the required hexagon.
113
'/ \ 0
0 R
/ , / \
~
Fig.6(f)
Let ABCD be the square and Rand U be points on
the 1 ine through the midpoints of AD and BC. Let P, Q, S
and T be the points of intersection of the circles. The
PQRSTU is the required hexagon.
Let a be the length of the side.
of UR a
Length ::: a + 2.6
4a ::: T
radius of 2a = 3 the circle
114
AOPQ is an equilateral triangle, since the sides
roe radii of equal circles.
the side of the hexagon = the radius the circle
2a = 3
perimeter of the hexagon 2a
6 = 3" x
= 4a,
which is the same as the perimeter of the square.
6.8. CONSTRUCTION OF AN OCTAGON WBOSE PERIMETER IS
(APPROXIMATELY) EQUAL TO A GIVBR SQUARE
of
The method of constructing an octagon is given
in the following lines.
k~~tre tatra samantato dinakaram~am nyasya turyasrit~
kOn~bhy6 bhujasGtrake~u nihitai: svai: karQQasutrarddhakai:
dvau dvau dik~u jha~~n prakalpya makar~~vasphalitai rastabhi: ..
aOtrai riswaradinmukhe vi racaye da9Ui~rakuQQam sudhI:
(Tantrasamuccaya(1S), patalam 12, sloka 32}
115
ie, construct another square circumscribing the given
square by extending each side by 1/12th of the length
of the side of the given square. Put two marks on its
each side by drawing circles with centre at the corners
and radius equal to half the length of its diagonal.
Form two fish 1 ike 1 ines (intersect ing ci rcles) on each
side by drawing 8 circles with centres at these points
and join these points successively to get the required
octagon [cf Fig.6(g)].
Fig.6(g)
116
Let ABCD be the given square and A'B'C'D' be the
circumscr ibing square. A'C' is the length of the
diagonal and OA' is the half the length of the diagonal.
Let the circles with centres at A',B',C' and D' and
radius OA' cuts the sides at P,Q,R,S,T,U,V and W. The
circle with centre at P and radius PR passes through R
and V. Similarly, by drawing circles with centres at
the other seven points will give 8 points of intersection of
circles (four fish like lines). Joining these points
successively we get the required octagon.
Let the length of the side of the square ABCD be
a. Then length of the side of the square A'B'C'D' will
be
A'B' 2. a
= a + 12
= 7a ""6
Length of the diagonal A'C' 12 .~ a =
.- 7 a OA' = '/2.12
PO = Length of the side of the A'B' 2A'P = -Octagon
117
AP = QB'
== A'B' - PB'
== A'B' - OAf
7a [2 7 a = - 12 6
7 a(2 - (2) == 12"
2A'P 7a(0.586)
== "6
PQ 7a 7a(O.586)
== -6 6
7a(0.414) == "6
when a == 6 cm,
PQ == ~ x 6(0.414)
Perimeter of the octagon= 8 x 7(0.414)
= 23.184 cm
But the perimeter of the square is 24 cm. Hence the
perimeter of the octagon is less than the perimeter of
the square.
118
6.9. THE RETHOD OF INSCRIBING AN OCTAGON (ETTU PATTAM)
IN A GIVEN SQUARE
The method is described in the following lines.
yasya vistaramarkk~msam
baQ~m~am pattam~va Ca
saptarn~~na dvibhagattu
karttavyarn k~Qabh~gikam
(Balaramam, page 59)
Divide the side of the square into 12 equal parts.
Retain five parts in the middle and delete 3~ parts on
either end of the sides of the square to get the required
octagon [cf Fig.6(h)].
H
5
Fig.6(h)
E R
D
119
Let PQRS be the given square of side a. Divide
each side into 12 equal parts. AB 1S the middle portion
of PQ having length Sa
PA BQ 3~ parts each. a 12· = =
Similarly we get CD, EF, and GH on each side of length
Sa 12· Draw line segments BC, DE, FG and HA to get the
octagon ABCDEFGH inscribed in the square.
Let the leng th of the side be 12 un its.
AB = 5 units. From triangle BQC, we get,
BQ2 + CQ2 = BC 2
3.5 2 + 3.5 2 BC 2
12.25 + 12.25 = BC 2
BC :;::: j 24.5
= 4.949, approximately
Or from the right angle triangle BQC,
Sin 45
1
12
BC
=
=
=
3.5 BC
3.5 BC
3.5 x J2
= 4.949, approximately.
Then
120
This value of BC is very close to 5. For practical
purposes the above value is acceptable.
6.10. METHOD OF CONSTRUCTION OF 'SRICAKRA' (OR SRfYAHTRA)
From the mathematical point of view, Sricakra
is an ancient geometrical portrayal consisting of a
bindu, ang les formed by the intersect ions of tr iang les,
8 and 16 petalled lotus, circles and squares (bhupura).
The method of construction of 'Sricakra' is explained
in Tantrasamuccaya (Silpabhagam) (16 ) in three verses.
The first verse describes the method of drawing lines
for bhiipura (squares), circles and the required number
of petals 'of lotus. The rule is stated in the verse
below.
~aQQavatyamgulay~mam sutram prakpratyagayatam
caturbhiramgulai: §i~tai: suvrttani ca bhGpuram
antarnavangulam proktam maddhye patram, tu ~o9a~a
~kadasamgulOp~tama~tapatram vidhiyate.
(Tantrasamuccaya (Silpabhagam), Annexure I(F), sloka 1)
This means that draw a line of length 96 angula
(about 288 ems) in the East-West direction on a plane
121
where the Sricakra is to be constructed. Draw three
squares for bhupura through the ends of the line and
three circles inside the square with the diameter of
the outermost circle is equal to 46 angula. The squares
and circles must be within a width of 4 angula (1 angula
= 3 cm). Then 16 petals of width 9 angula and 8 petals
of width 11 angula are to be constructed inside the
circle.
The next verse describes the method of drawing
the angles at the middle portion. The 'Katapayadi'
system is used in representing the numbers in this
verse. The verse is given below (16) .
vy~s~ 'de, vi' kfte ta, tta, ma, la, la, vi, ga, te, ca, ~a, bhage 'jha' sOtran
kFtv~ 'pu, ri, da, ~a, 'nt~ ga, va, va, la, mubhayo 'rvva', ta 'ye stoya bhagan
'dhanyam' 'nme' pravrjya grathayatu varuQa sadi sGtradvay~ni
pr~kpotam' r~,dhi' g~nam vi,di ma,tha dhuginam di,vya sunum ciram prak
The diameter (remaining part of East-West line)
of the circle inside the 8 petals is divided into 48
parts. Draw 9 lines ln the North-South direction
122
(perpendicular to the East-West line) cutting the East-
West line at widths of 6 parts, 6 parts, 5 parts, 3
parts, 3 parts, 4 parts, 3 parts, 6 parts, 6 parts and
6 parts in order from the west side. Delete segments
of 1 ines of length 3 parts at both the ends of 1st and
9th
lines, and remove 4 parts from both the ends of 2 nd
and 8th lines. Remove 16 parts each from both the ends
of 4th and 6 th lines and delete 19 parts at the ends of
5th l' Ine.
To form the angles, join the ends of 1st line
segment to the midpoint of 6 th line from the west.
Similar 1 y, join the ends of 2nd line to the midpoint
of 9 th line. Join the ends of 3
rd line to the point
on the circle when the East-West line meets the circle
and join the ends of 4th 1 ine to the midpoint of 8 th
line and the ends of 5 th 1 ine are join ed to the midpoin t
of 7th line.
From the other side join the ends of 9 th line
to the midpoint of 3rd
line. The ends of 8th line are
joined to the midpoint of 1st line and the ends of 7th
line are joined to the point of intersection of the East-
West line with the circle. The ends of 6 th line are
122(al
SRICAKRAM
!w
I:'
- -----_. -,-
Fig .6(i)
I ahupura trai(3 squares) v~ttatrai (3 circles) 9oda~adala (16 petals) A9tadala (8 petals) 42 Angles Bindu Triangle
123
joined to the mid point of 2nd line. Then the East-West
line is rubbed off. Then we get the angles at the
middle of the Sricakra [cf Fig.6(i)].
The resulting Sricakra consists of the following
elements as given in the third verse(16).
bindu, trik0l}a, vasuko~a, das~rayugmam
manvasra, nagadala, ~~9a~a, kar~oik~ram
vfttatrayam ca, dharani valayatrayam ca
SrIcakram~taduditam parad~vataya:
The cakra consists of a point at the centre which
is inscr ibed in a tr iang le. This triangle is surrounded
by 8 angles, 10 angles, 10 angles and 14 angles 1n
. order. Then there are 8 petalled and 16 petalled lotus •
All these are enclosed in vrttatria and in the three
squares (bhupura) . This is known as the
bhuprastaracakra.
Sricakra 1n the three dimensional form is called
Merucakra.
6.11.
124
TO FIND THE LENGTH OF THE DIAGONAL OF A SQUARE
WITHOUT USING PYTHAGORAS THEOREM
The method is given in the following lines.
Yasya vistaram suryamsam
paneamsam yuktam~vaea
tasya yOga~satOssutram
karQoamanam vidhiyate
(Balaramam, page 56)
Div ide the length of the side of the square into
12 parts. Add the length of 5 parts to the length of
the side of the square wh i ch give the 1 eng t h of the
diagonal of the square (approximately) [ef Fig.6{j)].
r-____________________ ~.c
a
a
Fig.6(j)
125
Let a be the length of the side of the square
ABeD. By this
5a given by a + 12 ::
the diagonal is
method, the
17a When
12
17 cm. By
diagonal of this square is
a :: 12 cm, the length of
using Pythagoras theorem,
the length of the diagonal is 12 a :: /2 x 12 ie,
d = 16 • 9705 cm . The difference between the two values
is very small.
By the above method the length of the diagonal is
a + 5a 12
(when a
= 12 + .416 x 12,
== 12)
== 12 + 4.999
= 16.999, nearly.
Hence the difference between the two values is
nearly .029 which is very small for practical purposes.
Further, if fia :;:
then !2 ==
17 a, 12
17 12
:= 1.416,
which is a very good approximation of the value of the
irrational number Ji.
6.12.
126
CONSTRUCTION OF LAMBA AND VITANA (VERTICAL AND
HORIZONTAL DIRECTION)
Let PQ and represent the dhwaja sutra
(kotinGl) on the rafter and the wallpla te respectively.
Consider a rectangular wooden board ABeD whose width
AB is 5/9 the w id t h 0 f the r aft er, i e , eq u a 1 tot h e
width of the rafter above the dhwaja sutra. This board,
known as 'mattam', is placed along the dhwaja sutra with
its long side coinciding with it [cf Fig.6{k) ](~3)
p
Fig.6{k)
It is pushed upward until its vertex B just
touches t he wall p 1 at eat B • Put a mark Q' on the upper
edge of the mattam where it meets the point of
127
intersection of the dhwaja sutra and wallplate.
Let I be the point on the dhwaja sutra at which
the lamba and vitana are to be determined. The Imattam l
is pI aced along the dhwaj a Sll tra in such a way that its
vertex B is at I and its upper edge coincides with
x
Pitch line. --(Kotinool)
Seat cut - - -(birdls mouth)
line (Lamba)
·-Horizontal line (~'itana rekha)
Birdls
Straight rafter (Common rafter)
Fig.6(l)
the
128
upper edge of the ra f ter. Put a mark at E on the edge
of the rafter when the point QI
with the rafter. Join Er and
lower edge of the rafter at F.
on the mattam coincides
produce
Then
it to meet the
EF will be the
horizontal line (vitanam) and the line perpendicular
to this 1 ine is the li'l.mba (perpendi cular 11 ine) through
I [cf Fig.6(l)].
Thus the horizontal line (vit~nam) and vertical
line (tukku) are drawn with the help of a mattam and
an axe. The simplicity of this method is that
mathematical computations are completely avoided.
However, the length that is to be cut off from
the lower edge of the rafter in order to fix it wi th
the ridge may be cal cula ted from the above f igu re. Let
XZ represent the plumbcut and .I... be the incl ination of
the rafter with the wallplate YZ in the length to be
cut off from the lower edge of the rafter. r t can be
seen tha t lYXZ and ~ XYZ is a right angled
triangle.
YZ Xy
129
= tan .,£.
YZ XY tan.l
XY is the width of the rafter and ifr:i= 45°, then,
YZ = XY
In Manu~yalayacandr ika, the incl ina tion is stipulated
as 45 ° •
6.13. GEOMETRICAL METHOD OF FINDING
RAFTERS
THE LENGTH OF
The method given in Manusyalayacandrika (54) is
explained below. Consider a square wi th side equal to
half the breadth of the house on a smooth plane or
ground. Let the horizontal side of the square represent
upper side of the cittuttaram and the vertical side be
the koti. Draw three lines parallel to the base of the
square representing the lower sides of cittuttaram,
wallplate and eaves one below the other in order. If
the house is a square one, the roof will be in pyramidal
shape. Now determine the number of rafters and gaps
between them on one side of the roof and mark their
130
positions on the wallplate in such a way that a gap
occurs exactly at the centre of the wallplate. The
number of gaps (pan t i) wi 11 be one less than twice the
number of rafters. Hence they will be in odd number
and the number of rafters will be in even number. Since
there is no rafter perpendicular to the wallplate, all
the rafters will be inclined rafters on each side
together with the four hiprafters.
pt---------------------~
Ar---~----~----~~~ G~----~----~------~~~J C~----_r------~------~~ O~ ____ ~ ______ ~ ________ ~~ __ ~~----~
Fig.6(m)
131
To find the length of the inclined rafters the
procedure is given in the following lines.
Iti vik~tilupanam pafikti makalpyatattal
sthitiniyamakrtanko yattadakranta karOQam
niyata kFtalup~lambadathakutapar~vam
bhavatipathagamr~am dirghamanam lupanam
(Manusyalayacandrika, chapter 6, sloka 19)
After fixing the positions of the rafters, the
marks on the wallplate are joined to the upper end of
the koti and produce them to meet the lower tip of the
roof - the 1 ine represent ing the lower tip of the roof
as in the above figure [cf Fig.6(m)]. Construct
rectangles with these lines as bases and koti as the
other side. The diagonals of these rectangles will give
the lengths of the incl ined rafters. I f the height of
the roof is less or greater than hal f the width of the
house, then the koti of the above rectangles must be
decreased or increased accordingly.
In the above figure BBI, CC' and 60' represent
the lower levels of cittuttara, wallplate and eaves.
Q, Rand S are the positions of rafters. Then PQ', PR'
132
and PS' are the lengths of corresponding rafters.
In this method there are two systems of right
angled triangles, one on the horizontal plane and the
other on a vertical plane.
is on a hor izontal plane.
In the above figure 4 OPQ
PQ is the hypotenuse of the
60PQ, which is the base of right angled triangle in
the vertical plane whose hypotenuse is the length of
the inclined rafter. In the same manner we can find
the leng th of the common rafter. The diagonal of the
rectangle whose base is OP and AP as the vertical side
will give the length of these rafters.
6.14. GEOMETlCAL METHOD OF DETERMINING THE WIDTH OF A
RAFTER
In general, there are two types of rafters,
namely, stra ight rafter (or common rafter) and incl ined
rafter. The width of the rafter is proportional to the
width of the wallplate (uttara). In the case of common
rafter (Nermancu) the width is taken to be equal to that
of the wallplate. This may be diminished or increased
by 1/8, 1/7, 1/6, 1/5, 1/4 or 1/3 of the width of the
wallplate. There are practices of selecting the width
133
1 3 2 of the rafter as 1~, 14 or times of the width of the
wallplate. Its thickness may vary from one angula to
6 angula.
In the case of inclined rafter, the method of
finding the width is explained in Manusyalayacandrika
as given below. [cf Fig.6(n)]
S.-__________________________ ~
Fig.6(n)
Consider a square PQRS with side equal to the
width of the common rafter. PQ is the bhuja, PS is the
koti and OS is a diagonal of the square. Let T be a
=
=
j3a 2
2
135
This is the width of the hiprafter and the widths
of others are determined accordingly.
But another version of the Manu~yalayacandrika
states that the width of the hiprafter is the same as
the diagonal of the square.
ie, width of the hiprafter ~ QS
== fi a
Thus the width is determined in two ways.
Evidently this value is greater than the previous one.
************
APPENDIX
ENGLISH TRANSLATION AND
SANSKRIT TEXT OF MANUSYALAYACANDRIKA
MANUSYALAYACANDRIKA . (English Translation)
Chapter I
I
In Rajarajamangalam temple, two divine powers in
the forms of Srikrisna and Narasimha glistens eternally
in unison.
2
May the divine powers glistening enormously in
temples at Trkkandiyur, Tirunava,
Mallivihara, Alathiyur, and Srikeralapuram, shine
unitedly in my mind.
The author prays for the blessings of the Supreme
power.
3
Ganesa, the refuge of all good people, the
recipient of extreme love of Nilakantha and son of
MANU~YALAYACANDRIKA
(English Translation)
Chapter I
1
In Rajarajamangalam temple, two divine powers in
the forms of Srikrisna and Narasimha glistens eternally
in unison.
2
May the divine powers glistening enormously in
temples at Trkkandiyur, TFprangode, Tirunava,
Mallivihara, Alathiyur, and Srikeralapuram, shine
unitedly in my mind.
The author prays for the blessings of the Supreme
power.
Gane~a,
recipient of
the refuge
extreme love
3
of
of
all good
Nilakantha
people, the
and son of
138
Parvathi, the giver of all wi shes of h is devotees,
respected by all and having abode at the great Srfmangala
temple, shines prosperously.
4
One who takes refuge only in the padakamala (lotus
foot) of that Ganesa and is inspired by the immense
blessings of his great teacher (guru) in learning various
subjects, becomes active wi th self-determination for
educating the pupils.
The au thor beg ins to wr i te th is tex t for the use
of the disciples.
foot)
srutis
5
I always prostrate before
of those brahmaoas whose
can describe the body of
Siva) in imagination.
the pad-kamalas (lotus
intellect indulgent in
even Parame~wara (Lord
139
6
After saluting the Brahma, the Adipuru~a,
(firstborn man) who is spontaneously ingenious in all
types of architecture this 'Manusyalayacandrika' is
written by me for the use of those of lesser intelligent.
7
Two Mayamatas, Pray~gamanjeri and two
Bhaskar!yams, Manumatam, Gurudevapadhati, Sr!harlyajanam
and such other famous texts (sastras) prosper.
8
After seeing the two
Ratnavalisaras of Parasara and
of Kasyapa and Viswakarma,
texts
Murari,
of MarkalJQeya,
Matas (opinions)
Kumaragama, HarisaIhhita
(Vishnu
various
Samhita) with explanations, Vastuvidya
briefly (this
and
text other texts I summarise here
on V~stus~stra) as given in Tantrasamuccaya.
9
Firstly, one who belongs to BrahmaQa or other
castes and desires to construct a house must adopt a
140
local brahmat;la (Acarya) of all noble qualities. He
determines the bhGmi suitable to one's caste and then
performs vastupuja (offerings) and such others on this
bhumi. After this the house is to be constructed by very
eminen t artisans (~ilpins) as stipulated in the
v~stusastras.
10
These brahmaQas (~ch~ryas) after considering the
saying in Vedas, Agamas etc, prescribe the rules for
constructing houses and temples. It is the duty of the
craftsmen to mix or join earth, stone etc, in all the
buildings under the advice of these Acharyas.
11
Depending on the nature of the work the artisans
(Bilpins) are classified into four categories, namely,
Sthapati, SCitragrahi, and Vardhaki. These
artisans, who are experts in the ir respect i ve fields are
to be selected properly.
12
One who is an expert in all crafts prescribed in
every sastra, well versed in all the sciences, always
disin terested, free from the vices 1 ike envy, compet i t ion
141
etc, truthful, just and clean may become the Sthapati.
13
It must be known that Sthapati is the competent
person in constructing the building. Then either his
son who is almost equally competent or one of his
disciples who is able to understand his mind properly
may become the Siltragrahi. The person who reduces the
size of materials to the appropriate size is known as
the TakoiJaka and he must always be happy. One who is
always careful and an expert in the craft of assembling
pieces of timber and other materials is known as
Vardhaki.
14
Without these four types of ~ilpins like Sthapati
etc, the construction of houses and other buildings is
imposs ib1e. Therefore a most intell igent brahmar;ta
(Acharya) must get the house built by them after pleasing
them properly.
15
Misfortune wi 11 occu r to those who are 1 i v ing in
houses not properly constructed (wi thout proper lak~al)a).
142
So the entire work from beginning to end should be
decided mentally and then proceed doing it.
16
In constructing a house, the testing of bhumi in
several
choice
ways, the determination of
the
directions etc, the
the of auspicious vith i, formulation of
measurements of the house, determination of parts of the
house like ankal)a, kuttima etc, and, in a similar way,
the formulation of rules regarding outhouses etc, are
to be done in successive order.
17
An even ground which is bl essed wi th the presence
of cows, human beings, trees bearing flowers, fruits and
milk, slightly inclined to the East, smooth, having
having
having
majestic sound, water course flowing to the right,
large quantity of earth and seeds growing rapidly,
equal cl ima t i cal cond i t ions ei ther in hot or
and wi thout shortage of water 1S described
suitable (uttama) for the construction of
cold season,
as the most
houses. A
bhumi whose characteristics are opposite to these is
least suitable (adhama) and bhumis which satisfy some
of these characteristcs and not the others are medium
(madhyama) •
143
18
The bhumis which are in circular or semicircular
shape, having 3, 5 or
of sula or sGrppaka,
6 angul ar corners,
like the upper side
in
of
the shape
fish, or
elephant or tortoise, like the face of a cow, having
hollow
bone,
depression at the
inside containing
centre, having cavities or
ash, charcoal, husk of grain,
hair, worm, termite hill etc, having bad smell and which
face unf avou rable direct ions (v id iks) are to be rej ected.
19
The bhumis which are low from East onwards and
high from West onwards are the eight vithis, namely,
G5vu, Vahni, Antaka, BhITta,
and Dhanya in their order.
prosperity, loss of money,
wealth, poverty, loss of
Vari, Phapabhrth,
These bhQmis will
self-destruction,
Matanga
provide
loss of
son, wealth, and mangalam
respectively to those who are residing in them.
20
Bhtlmis having depression at the centre will cause
exile and
destruction
hav ing mounds
of weal th and
at the
happiness.
centre will cause
BhGmis which are
144
slightly low towards Agni (South-East) corner and upto
Vayu (North-West) corner may generally give poverty.
21
In a middle elevated Dlot the first constructed
house will give pros~erity for ten years. The east
elevated as well as South-East elevated plot will give
prosperity for hundred years. The prosperity remains
for thousand years or half of it according as the house
is on a plot wi th Ni~Tti (South-West) corner or western
portion elevated. If the plot is
(North-West) corner/ northern side
corner the prosper i ty remains for
elevated
or IBa
12 years /
on its Vayu
(North-East)
8 years or
100 years respect i vely. The resul ts prescr ibed for each
plot (bhumi) in the above verse will be effective only
after the completion of these periods defined in this
verse.
22
Ilafifli and Baniyan trees on the east side of the
house, the country-fig (Atti) and Tamarind tree on South,
provides prosperity. The Pipal tree and Ezhilampala
(saptaparr,taka) on the West side are considered
auspic ious • The trees like Naga and Itti on the North
145
side are cons idered to be fortunate. Jack tree, Arecanut
tree, coconut tree and Mango tree on the four sides of
the house from the eastern side onwards, considered to
the owner of the house to have special prosperity.
23
The Peepul tree which occupies a position
different from its prescribed position will cause
difficulties from fire. The Itti tree situated in the
wrong position brings many sorts of
the Baniyan tree makes difficulties
manias. Similarly
from enemies, Atti
generates stomach diseases. Trees which are not in their
prescribed positions and those whose heights exceed their
distances from the house are to be cut off even if they
are precious.
24
The presence of trees like Kumizhu, Kuvalam
(crateva reI ig iosa), Katukka (Terminal ia chebula), Goose
berry, Fistula, Devatara, ~ami (Plaksa), As6ka, Sanda~
wood, Punna (Callophyllium), Vefina (Avicenna), Campakam,
Karinnali (Mimosa catechu) etc, on the rear and other
two sides are auspicious. Similarly, the growth of
Jasmine, betal v ine and such other plants, planta in etc,
146
on all sides of the house is conside~ed auspicious.
25
Jack tree and such othe~ t~ees having internal
core (antassa~a). Trees like Tamarind, Teak etc, a~e
having internal and external core (sarvasara t~ees).
Palm, coconu t tree, a~ecanu t palm etc, a~e wi th ex ternal
core (bahirssara trees).
Ezhilampala, Silk-Cotton
The d~um-stick stree (Murinfia),
t~ee, Murikku (E~ithrina Indica)
etc, are coreless t~ees (Nissara trees).
Out of these, the trees of the first type a~e to
be planted in the middle of the space between the house
and
cores
its boundary.
( Sa rv a sa r a )
Trees having internal and external
are to be cultivated in a region
exterior to the first type and the othe~s are to be
planted outside the region of the second type.
26
T~ees like Kanjiram, Ceru (Marking-nut tree) ,
. Vayyamkata, Naruvar i,
tree, Euphorbia
SwarQQaksheeri, are
Taf'1ni, Uka (tooth brush tree),
(Kallippala), Karamussu
not at all permissible inside
Neem
and
the
plot. The drum-stick tree is not permitted within the
147
prescribed boundary of the house.
27
It is dangerous to construct houses on the left
and rear sides of the abode of Lord Visnu and on the
right and front sides of Ugramtirthis (violent deities)
like Kali, Narasimha, Siva etc. If the deity situates
in a lower region, then the houses on the right and front
sides are dangerous. It is not considered auspicious
to have the heights of the houses higher than that of
the abode of the deity. Those who are the dependents
(attendants) of the deity may build their houses near
to the deity except on their prohibited sides.
28
Houses in the immediate neighbourhood of farm,
mountain, temple, sea, river, hermitage and stable are
dangerous in many ways. The house hav ing height equal
to or less than the height of temple is more auspicious.
Houses having heights greater than it or having two
storeys are not at all advisable.
148
29
Bhumis hav ing Kusagrass I Darbha I Karu ka, and Ama,
having equal
increased by
length and
1/8th
, l/6 th
breadth
and 1/4th
(square) I length
parts of breadth,
having colours wh i te, red, yellow and black I hav ing the
smell of ghee, blood, rice and alcohol and having tastes
sweetness, ast r ingen t, bi t ter and pungen cy are prescr ibed
for brahmaQas and others in order.
30
The bhumi which is inclined from south to north
and containing an Atti tree on it is auspicious for
brahmins. BhGmi whi ch is incl ined from wes t to east and
with a pipal tree on it is suitable for K~atriya. The
bhumi wi th a slope towards west and wi th a Ban iyan tree
on it is recommended for Vaisya. If the bhumi prescribed
for the Vaisyas contains an Itti tree on it then it is
appropriate for 'Sudra. A bhumi which contains an Itti
tree on it and having slope from north to south is also
suitable for Sudra. I f the bhumi is of opposite type
then it is not suitable for any of them.
31 The bhumi which is of mixed character with respect
to the colou r, smell and taste is to be rej ected by all.
149
When the natu re of the bhumi is not known it is to be
tested at night by using nimittam (omen) in the
prescribed method.
32
Make a piton the bhumi and place an unbaked clay
pot filled wi th I dhanya ' . Its mou th is closed by another
mud-pot and pour ghee into it. Four wicks in whi te I red I
yellow and black colours representing four var~as
(castes) in order are placed in the pot
that the white wick is directed towards
other wicks in the remaining directions.
in such a way
east and the
The wicks are
lighted in order accompanied with 'mantratantras I. After
a short while, see which of the four wicks is still
gleaming. Then the bhGmi is suitable for the caste
represented by the colour of the wick. If all the wicks
are glowing then the bhurni is suitable for all castes.
33
Make a pit on the bhurni and fill it with water.
Drop flowers of phlomis (thumpappuvu) and such other
flowers into it. The clockwise movement of the flowers
is auspicious where as the anticlockwise movement is
inauspicious. If the flowers remains on the (NW..ES) sides
then it is good and if they remain at the corners then
150
it is bad. After understand ing the mer i ts and demer i ts
of the bhumi in this way the intelligent sthapati has
to get the bhumi properly levelled.
Chapter 11
I
The selected bhOmi is to be properly levelled
using the apparatus like avanata or such others or by
water fill ing method by expert craftsmen. Then a un iform
cylindrical strong wooden rod of ~ kol (36 cm) length
is to be constructed with its lower end of diameter 2
angu1a (6 cm) and upper end of 1 angu1a. The tip of the
rod must be in the shape of the bud of a lotus flower.
This rod is named as 'sanku'.
2
Draw a circle using a rope whose length is double
that of the 'sanku'.
the circle accurately,
point.
After determining the centre of
fix the sanku firmly at that
151
3
In the morn ing , when the image of the tip of the
~anku just touches the circle on the west, one (sthapati)
who is disinterested must put a mark on the circumference
of the circle. Similarly, put a mark on the opposite
side (East side) in the afternoon. Put another mark on
the West side al so the nex t morn ing . Di v ide the arc
length between the two marks into three equal parts.
Then t he mark wh i c h is nearer to the first day's mark
will be the accurate mark on west side.
4
The line (sutra) through these two points which
are determined on two consecutive days as explained
above, will generate the East and West directions very
accura tel y •
5
The line (sutra) which is well defined in the
middl e of the bhGmi (k 9 ~t r a ) as ex p I ain ed above is call ed
the Brahma sGtra. Construct two intersecting circles
in the middle of this line (sutra). Determine a line
through the middle of the fish-line (intersected circles
152
form curve in the form of a fish} which is detained
crosswise due to the intersection of those circles. This
line in the South-North direction is called the Yam a
sutra.
6
After determin ing the Brahma sutra and Yama su tra,
mark a point on each of the four branches of the two
intersecting sutras at a fixed distance from their point
of intersection and with these points as centres draw
four equal circles intersecting in pairs. Here, in
corners, four
intersections
f ish shaped
of pairs of
lines are
circles.
formed by the
Draw two lines
passing through the middle of the f ish shaped 1 ines in
pairs having their terminal ends at the If:la {North-East}
and Agni (South-East) corners and a square is drawn
accordingly.
7
The square bhumi (square maQQala) is then div ided
into four quadrants (kha09as) by the two 1 ines (sG t ras)
hav ing thei r
Isa khaI1Qa
terminal ends at
or Devakhal]qa
the East
may be
and North sides.
prescribed for
153
construct ing houses for BrahmalJa and others. If the area
of the bhumi is too large then each quadrant may further
be divided into 4 parts (sub khal)gas). Then the Nirrti
part in the lsa khal)ga and Isa part in Nirrti khal]9a are
suitable for the construction of houses.
8
When the bhflmi is divided into four kharyc;1as, the
Isa kha~~a (North-East) is known as the Manu~yakharyqa
which prov ides prosper i ty and Nirrti . (South-West) khal)9 a
is named as the Devakhal)qa which gives favourable results
to the residents of the house. These two khandas are . . auspicious for the construction of houses for man.
9
(South-East khal)9a) is named Yama
khal)ga. This provides death (destruction) to the family
and therefore is to be avoided by all castes. The Vayu
khal)c;1a (North-West khanda) is known as Asura khal)c;1a wh i ch
is not auspicious for the construction of houses. But
in some places, it is accepted for the construction of
houses for Vaisyas.
154
10
After delet ing the el onga t ions of the bhGm i
prescribed for K~atriyas and others its middle portion
is made into a square. The two diagonals having initial
points at Nirrti and Vayu corners and terminal points
at Isa and Agni corners respectively are known as rajjus.
11
The intersections (or coincidence) of the ends
of Brahma sutra, Yama sutra and Rajjus with the central
axes of house, well, tank etc, will cause difficulties,
except in the case of Catu sScH a wi thou t el onga ti on
(Mukhayama) to the ankaQa.
(The intersection or coincidence is known as vedha)
12
The results of V~dha (intersections of axes as
in the above verse) from east direction onwards are
separation from husband, leprosy,
enemies, loss of son, loss of
complaints, loss of family, and
(agricultural products) respectively.
difficulties from
wealth, rheumatic
loss of grain
155
13
If the 11:3 a khanda or any other khaI')9 a of the
ksetra (bhumi) is divided into 9 x 9 padas (cells), then . it is known that the widths of the Sutras and Rajjus are
given by 1/12 of a pada. Similarly, when it is divided
into 10 x 10 padas, 1/8 of a pada will be the width of
the sutras and rajjus. If the khanda is divided into
8 x 8 parts then their widths are given by 1/16 of a
pada.
14
The mutual intersections (v~dha ) between the
central axes of houses, ankaQa (courtyard), well, tank,
door etc, and the vedhams between the rajjus and the
diagonals of the corner houses are to be avoided.
15
To determine the width of the vlthi (envelopes)
there are several types of da~9us, depending on the area
of the bhumi. For this, the height of the owner of the
house is taken as I tiUam' . Three types of daQ9us are
defined by taking its length 10 talarn, 9 talam or 8
tal am. If the bhumi is of sufficiently large size then
anyone of these three da09us is taken as the width of
the vlthi.
156
16
By dividing
be nine expanding
outermost to the
in t 0 18 pu tas (calyxes), there wi 11
envelopes (av.rtti) of which from the
innermost are the vithis of Pisaca,
Deva, Kub~ra, Yama, Naga, Jala, Agni, Vinayaka and Brahma
respect i vely. Of these, the v i this of P i~aca, Agn i, Naga
and Yama are considered to be inauspicious for the
construction of houses on the four sides.
17
It is best (uttama) to have the width of the vithi
as l~ times the length of the ankal)a (courtyard) which
has already assumed in building the house. It is
madhyama (intermediate) when it is equal to the length
and it is adhama (worst) when it is less than the length
of the ankaQa. In small
may be taken as hal f of
such case the houses on
plots the width of the vithi
the length of the ankal)a. In
the east and north sides will
have to include also the J al a vi th i wh ich is a spec i al
case of determining the width of the vithi.
18
In some places, it is seen that, catussala
(courtyard houses) is constructed in a very small plot
157
with a prescribed shift (gamana) of its centre from the
point of intersec t ion of the Brahma sut ra and Yama sutra.
Since the vlth is are too small, the mer its and demer i ts
due to them will be negligible. Hence the division of
the bhumi into khal)c;1as 1 ike Isa, Agni etc, and v ith is
like Pi~aca, Deva etc, are considered unnecessary.
19
The width of the v rth i is determ in ed by l~ times
the length of the ankana . and 18 times the width of the
vithi will be the width of the bhGmi (plot). Thus from
the centre (anka~a) the measure of the bhumi may be
determined. I f the house is si tua ted in a bhumi whose
boundary is not known it may be calculated from the
length of the anka~a of the house. After determining
the boundary of the house, the boundary wall may be
constructed (appropriately to the status of the owner).
20
After combining the vlthis of Brahma and Gan~sa
together in Isa or Nirrti kha~9a, that region (Vastu
pada) is d i v ided into 81 padas or 64 padas or 100 padas
as ment ioned earl ier. Here, the parts (organs), marmmas
(nodal points), and deities of the Vastu are to be
determined accordingly.
158
21
In 81 pada system there are two sets of Nadis ,
(lines) containing 10 Na~is each with their terminal
points on the east side and north side respectively.
Similarly, there are two sets of rajjus each set having
5 raj jus pass ing through 9 padas, 6 padas and 3 padas
and having their terminal ends directed to the Agni
corner and I~a corner respectively. There are hundred
murmmas formed by the intersections of 8, 6, 5, 4 and
3 sutras occuring at the corners of the cells and they
have to be avoided in the construction of walls, pillars
and such others.
22
The difficulties due to the placement of walls,
pillars etc, at the marmmas, may be avoided by shift ing
their positions towards east or north by 1/24 of pada
from the marmmas. Anyhow, if the dif f icu 1 ties due to
marmmas occur, then the images of the heads of buffalo,
lion, elephant, tortoise and pig in gold must be
installed properly by a priest for the relief from the
difficulties.
160
26
The central position is occupied by the Brahma.
Outside the cells, there are Sarvaskanda in the east,
Aryamav in the south, Jrmbaka in the west and Pi 1 ipi ncaka
in the north of the vastu. Further, deities like caraki,
Vidarya, PG tan i ka and Paparak1}as i are pos it ioned at the
corners from Isa corner onwards.
27
There 1 i ved a demon (asuran) who was mos t arrogant
and an enemy to Devas. He conquered the whole world by
his wonderful courage and strength. In a battle with
navas he become weak and fell down to earth. Even then
he survived on the earth and troubled it by whirling
several times. So the human beings were unhappy and in
the same way the Sages and Devas became unhappy.
When
especially in
1 ike the sky
28
the vastupuru~a
city, town, vastu,
in small and large
flourished everywhere
k.!?etrakhar;l9a and ankaoa
pots, with his back on
earth, legs at the Nirrti corner and head at Isa corner,
the devas suddenly seated on his body permanently.
161
29
Isa resides on his head, Parjanya and Diti on
eyes, Apa on face, s im i 1 arly, ~pavalsa on neck, Jayanta
on right ear, Aditi resides on his left ear, Indra
situates on his left shoulder and Arggata resides on his
right shoulder.
30
Sun, Santhya and such others resides on his left
arm and Moon, Bhallata and others dwells on the right
arm. Savithav and Savitri occupies the left prako~ta
and Siva and Sivajith on the right prako~ta.
31
Mahidhara and Arya reside on his breast, Vivaswan
and Mi tra on stomach, Brahma on the navel, Indra on his
phallus (Mandrum) , Indrajit on v~9aQa (testicles) and
others reside upon his legs.
32
I f the dei ties res id ing on the Vas tu are properly
propitiated then they will provide favourable results.
162
Otherwise, they will produce bad results. So offerings
(VastupGja) are to be performed for propitiating the
deities on the Vastupurusamandala. . . .
Chapter III
I
The thickness of 8 gingelly seeds contained in
its shell is called a 'yavodaram'. Eight 'yavodaram'
constitutes a 'matrangulam'. v ita s t i i s de fin ed by 1 2
angulam. Twice the vitasti is named a kara (hasta),
Ki~ku, Aratni, Bhuja, Doh, Mu~ti etc. There are
different types of measurement (kol) based on the varying
length of an angula with the size of seeds and
increasing the length of hasta by 1 angulam each.
2
The measurements having 25 matrangulam is named
'Prajapathyaka' which is defined for measuring Vimana
and in some places it is also used for measuring temples.
The hasta of length 26 angulam is called 'dhanurmu~tikam'
and it is suitable for measuring for all houses and
temples (for all buildings).
163
3
The intellectuals (~ilpins) define the hasta of
27 angularn as Dhanurgraha. It is used for measuring
villages, markets, garden etc, and also for measuring
tank, lake etc. I t is used for measur ing all types of
houses wh i ch is ev iden t from its name. Dhanurmust i is,
also acceptabl e for measur ing the markets, garden, tan k ,
lake etc.
4
The hasta consisting of 28 angulam is called
. Pracyam.
Vaideham.
Vaipulyam.
The hasta cons t i tu ted by 29 angu 1 am is kn own
The measure formed by 30 angulam is called
Adding one angulam to this will get the hasta
named Prak i rnam.
hastas (kol 5) •
In this way there are eight types of
5
Dhanurgraha and Praklr~am are used for measuring
Brahmin's houses and Vaipulya and Dhanurmu~ti are
employed for measuring King's houses, palaces etc.
164
6
Prajapatya and Vaideha are used for measuring
houses and all other equi9ments of Vaisyas and Pracya
and ki~ku are prescribed for ~udras. In particular,
kisku is suitable for all.
7
It is not auspicious to kings and others to accept
the measures (hastas) which are prescr ibed for the upper
castes and not for themselves. All the measures which
are prescribed for lower castes are acceptable to
Vaisyas, Ksatriyas and Brahmins in order.
8
All the madhyama and adhama hastas which are
formed due to the differences in the measure of angulas
are acceptabl e in the case of templ es accord i ng to th e
situations.
said
9
The matrangulam which
to be the best (Ut tama)
is compr ised of 8 yavas
and wh i ch are compr i sed
is
of
7 and 6 yava are considered to be in termed i ate (madhyama)
and worst (adhama) respectively.
Angulams of
to
165
10
uttama, madhyama and
the measures of widths
adhama
of 8,
types
7 and occur according
6 sali(red-paddy or Navara) grains respectively. The
above three types may also be obtained from the lengths
of 4, 3~ and 3 sali grain respectively.
11
There will be 9 types of hastas of uttama,
madhyama etc,
of angulams.
8 types of
nature depending on the nine distinct types
These 9 types of hastas together wi th the
hastas as given in the above verse will form
72 types of hastas.
12
The kara (hasta) comprising of 24 matrangulam
which is defined earlier is auspicious for all castes
and situations. Other hastas are acceptable to all
depending on their respective castes and types of hastas
prescribed for them for different situations.
13
The measurements of house and others are expressed
in hastas (karas) itself and in some cases they are
166
defined in terms matr~ngulas. When it is impossible to
measure the length of the perimeter and gati (change or
shift) in terms of hasta and angula, it may also be
expressed in terms yavas. In houses and such other
buildings of human beings, the gatis (changes or shifts)
and boundaries of outhouses (upalayas), stable etc, are
measured in terms of I daQqu I of 4 hastas.
measurement is also known as 'ya~ti'.
daQ9u will be a rajju.
14
This unit of
Eight times a
Statue (idol) or such others are to be measured
using tlHam (a proportionate measure), yavam etc. Yavam
is to be used for measuring ornaments. Vitasti is the
unit of measure for measuring silk, blanket, cloths etc.
Arms such as sword, arrows etc, are measured us ing the
measu re (w idth) of two r ing-f ingers or by the width of
one ring-finger of their owner. The pots for sacrificial
(yaga) purposes are to be measured using the measure the
mu~ti of the master of the sacrifice (y~gakartta). Other
items are to be measured using the measure of pada
( foot) .
15
There are various types of v illages depending on
167
the number of houses of brahmins in a local i ty. These
villages are aga in class if i ed into ut tama, madhyama and
adhama types depending on their areas.
16
A reg i on of area of one yoj ana square is call ed
an uttama village. A village is said to be madhyama if
its area is half yojana square and it is said to be
almost adhama when the area is a quarter of yojana
square.
17
For towns (nagaram) there must be an area of
thousand to two thousand da~9us. Similarly, the region
having a sea shore with shipping facilities is called
a city (pattana).
18
A reg ion which is famous due to the presence of
a King's palace and merchants and such others is named
a puram (town). A reg ion hav ing palaces of kings and
residences for all sorts (varnas) . of people is famous
by the name nagara (city).
168
19
A brahmin' s family together wi th the subord inates
or assistants and their families living under the same
brahma~a (kara~avar) is called a village (grama).
20
Depending on the number of brahma~a houses in a
village and their extensions, the villages may be
classified into uttama, madhyama and adhama categories.
21 & 22
In temples, the external width of the prasada
measured along the beam is called the perfect (best)
dal)~u (uttama dar;tQu). Similarly, the measure along the
Jagati is the madhyama (intermediate) daQ~u and along
the padu ka is known as adhama (worst) dal,l9u. In temple,
outside the srikov i 1 (prasada) , five boundar ies are to
be determined using this daQ9u.
23
Ketuyoni is defined for all objects which are used
for transportation since it is auspicious in these
objects. Gajayoni is prescribed for cot or such other
169
equipments and for seat (pr~ham), stool etc, simhayOni
is recommended. In the case of box and such others and
in defining well, tank, lake, nest etc, the v!,~ayani and
dhwajayani are acceptable. Ketuyoni is prescribed for
all types of foundations such as the foundation of pipal
tree etc.
24
To determine the yonis of measur ing jar and such
other pots, tank, well etc, ankaQa, garbhagraha etc,
interior perimeters are considered. In the case of
Turyasra s~la (Madhyapraruda sala) the perimeter is
measured along the central 1 i ne of the width of the beam.
In all other cases yen is are det ermined wi th respect to
the exterior perimeter. The yoni defined using the
interior perimeter is sometimes called antary6ni.
25
Multiply the perimeter which is the sum of the
desired lengths and breadths by 3 and then divide it by
8. The remainder will represent the corresponding yoni.
If the product is divided by 14, the remainder will be
vyaya (expend i ture) • Then mul t iply the per imeter by 8
and divide it by 12, the remainder is the aya(income).
170
If it is div ided by 27, the remainder wi 11 be the sta r
(nak-t'la tra) and the quot ient is call ed the age (vayassu).
The rema inder will represent the ti t h i (pakkam) when the
product is div ided by 30. 1ft he prod u c t is d i vi d ed by
7, the remainder will be the day of the week. When the
perimeter is multiplied by 9 and divide it by 10, the
remainder will represent an alternate vyaya.
26
The eight yonis dhwaja, dhuma, simha, kukkura,
vf~a, khara, gaja and vayasa occur in eight directions
from east onwards in order. Of these, the odds will
provide prosperity and evens will cause misfortune.
27
Ketu (dhwaja) y5ni provides all favourite wishes
to the owner of the vastu. It has satvika quality,
represents the guru of devas (Jupitar) and is a brahmin.
Even though it is defined for the east side, it is
acceptable to all objects and especially in all
directions (it appears that in the last line it should
be 'abhihita' and not 'avihita ' ).
171
28
Sirilha yoni situates on the south side and
represents kuja. It has tamasa quality and is ksatriya
and provides prosperity. Gaja y~ni defines on north
side, represents Budha, having rajass quality and is a
vaisya. It provides fortunes.
Vf"~a yan i with tamo qual i ty situates on the wes t
side, represents Sani and is a sudra. It gives
prosperity 1n agricultural production. Then the yan is
defined at the corners are despicable (desertable).
29
Dhuma yoni provides anxiety, quarrel will be the
reaul t of Kukkura yoni. Khara yoni will generate
fickleness and K~ka y5ni will result in no prodigy.
Therefore, the corner yonis are to be avoided for the
construction of houses.
30
Ketu y~ni is prescribed for the east direction
and it is suitable for houses on any side. Sifuha yon i
is defined for houses on the south side and Ketu yoni
is also suitable for this side. Gaja yoni is suitable
for north siBa (house) and Ketu and Sifnha yon is are also
172
auspicious on this side. VF~a yoni will be on the west
side and Ketu, Simha, and Gaj a yon is are also su i tabl e
on this side.
prescribed
accepted.
for
For corner houses, the yonis which are
their related side-houses are to be
31
It is generally admitted that y5ni is the vital
air (prava) of all houses. Theref ore, su i table yon is
which are prescribed for each direction must be accepted
accordingly. In all houses 'the death' (due to the
selection of inauspicious yonis) must be avoided. If
the death (unfavourate yoni) is accepted then it will
cause several misfortunes.
32
In all cases the ayam (income) must be greater
than the vyayam
be the resul t.
(expenditure). Otherwise misfortune will
The merits and demerits of the star
(nak{3atra), yoga etc, are to be learned from astrology
and such others accordingly.
33
There are five stages of age (vayassu), namely,
173
bUya, kaumara, you t h, oldage and death. Out of these,
the last one is not auspicious in the case of houses.
Others are auspicious for the construction of houses.
34
Yoni, aya, age, naks;atra (star), tithi, ra~i, and
the castes, such as brahmaJ;,la and like others, are defined
in two ways. Vyaya is def in ed in 4 ways and the days
of week and dhruva etc, are explained in 3 ways. Out
of these,
accepted
the first
by all and
set of
the
definitions of yoni etc,
above definitions are to
accepted only if necessity arises.
35
are
be
Gen erall y, the prescr i bed yoni, aya etc, for each
are to be obtained from the perimf'ter. It will be very
prosperous to have the same yi;)ni etc, with respect to
the length, breadth, heights of pillar, padamana,
adhifrltana, and area of the house and also by the
alternate methods explained earlier.
36
In all houses, the measurements of length,
breadth, padam~na, pillar, adhi~tana, garbhagraha, door,
174
statue etc, beams like arudam and all different parts
of the two-storey building are to be determined with
respect to the perimeter of the main beam. If these are
determined by parts (divisions) as given in the alternate
method then they are to be adjusted to get the nearest
appropriate yonis.
37
The of the 1 ength and breadth is known
as area.
product
After
breadth in order
determining the appropriate length and
to get the des ired yan i, the vyaya, aya
determ in ed as in the case of per imeter. etc, are to be
This is also an accurate method.
38
It is mentioned earlier that the usual vyaya 1S
obtained by dividing the perimeter multiplied
14. Multiply the perimeter by 9 and divide it
8. Then the remainders will be the vyayas.
by 3 by
by 10 or
When the
nak~atra, determined by the prescr i bed rule, is d i v ided
by 8, the remainder will be the vyaya. Thus there are
4 types of vyayas. In all these cases, the vyaya must
be less than the aya. Otherwise it will cause disaster
to son, wealth etc.
175
39
Add one-third of the perimeter to itself.
Mul tip1y it by 2 and div ide by 8. Then the remainder
is the aya. Multiply the perimeter by 27 and divide it
by 20 I the rema inder is the age. The balya, kaumara etc,
are to be known by the quotient in order. The remainder
will represent the number of years passed over by the
respective age. Of these, the youth is the best age.
40
Di v ide the per imeter i tsel f or nine times of it
by 30. Then there remains the t i thi of the two pa~~as
(purvapara pak~as) as before. Multiply the perimeter
by 3 or 8 and divide it by 4, then the remainder will
represent the castes of brahmaQa, k~atriya and others
in order. When the perimeter is multiplies by 4 or 8
and divided by 12, the remainder will be the r~/si (month)
corresponding to that perimeter.
41
Di v ide the per imeter itself or 3 times of it by
7. The remainder is
Mul t ip1y the per imet er by
16. The remainders will
others.
the day of
2 or 3 and
the week (vara).
then divide it by
represent the dhruva and such
176
42 & 43
Add the number corresponding to the vyaya to the
area and divide it by 16. The remainders will represent
the dhruva, dhanya, jaya, vinasa, khara, kanta,
mamaprasada, sumukhatva, vaimukhyam, asaumyatva,
virodham, vittOlbhava, k~ayam, ctkranda, vJ;dhi, jaya
respectively. The result of each is implied in its name.
Chapter IV
1
Determine the appropriate length and anka~a of
the house in such a way that sui table yoni, aya, nak9atra
(star), age etc, are obtained from their respective
perimeters in all methods as explained earlier. Then
an expert person (architect) have to determine the leng th
and width
'I~tadirgha '
of part) so
of the house according to the rule of
(pref erred leng th) or gUr;tamBa (mu 1 t ipl es
that the intermediary spaces (antarala or
alinda} become small.
2 & 3
The per imeter of every house is obta ined from its
preferred length. The corresponding width is got from
177
this perimeter. Padamanam (height of the house from the
level of paduka to the level of wallplate) is obtained
from the width and from the padamana,
foundation is determined. The height
the difference between the padamana
the height of the
of the pillar is
and the height of
the foundation. From the height of the pillar, the width
of the beam (wallplate) is obta ined. Based on the width
of the each beam, the width of rafters, brackets (vamata)
etc, are to be determined. Similarly, the thickness of
beams, brackets etc, are to be obtained from their
respective widths.
4
The preferred length of 6 hasta or above is
multiplied by
added to this
8 and the corresponding yoni number
number. Then one-third of this will
is
be
the requ i red per imeter of the house. I f the process is
reversed, the length is obtained from the perimeter. When
the length is subtracted from the semiperimeter, the
width of the house is obtained.
5
Multiply the preferred length 1n hasta (kol) by
2 and add one-third of this to itself; Adding one-third
178
of the prescribed yani number to the above sum will
provide the perimeter of the house.
6
In a square house, 1/4th perimeter will be the
length which is equal to the width of the house. If the
semiper imeter is divided into 9 parts, then four parts
will be the width and
leng th of the house.
the rema in ing
Thi s is the
parts will form the
I padadhikam I. When
the semiperimeter is divided
will form the width and the
length. This is known as
into 10 parts, four parts
remain ing 6 parts form the
'arddhadhikam' . These three
types of divisions are prescribed for temples.
7
In houses (manu9yalayas) I the padadhikam d i v is ion
is accepted and in some cases,
by some. Arddh~dh ikam is
samatalam is also adopted
not recommended here (in
houses) .
provide
According to sages all p'ad5nam divisions will
calamities to all and hence they are not
acceptable at any cost.
179
8
I f the semiper imeter is d i v ided in t 0 12, 13, 14
parts or into 16, 17, 18 parts or into 20, 21, 22 parts
or into 24, 25, 26 parts or into 28,29, 30 parts or into
32 parts then the width is determined by 4 parts and the
remain ing parts form the length of the house. Thus the
sages def in es width in gunamsamethod from 8, 9, 10
div is ions
samatatam.
onwards except the
9
4th divisions of the
When the semiperimeter is divided into 11 parts,
the width may be determined by 3 parts and the length
by 8 parts. Width,
considered inauspicious
etc.
much
by
larger than ~
the sages 1 ike
10
of length is
Gargga, Dak~a
In the plan of a house (sala) there will be 4
detached side houses (Diksalas) and their respective 4
corner houses (Vidiksalas). Thus there are 8 houses
prescribed by sages for human beings. Depend ing on the
specialities in direction, measurement, name etc, of
180
beams in houses,
The measurements
houses are to
there will be 9 types of Salas (houses).
of the parts of the storeys of the
be def ined in accordance wi th the
measurements of the respective s~las (houses).
11
Salas are classified into two groups bhinna and
abhinna according to their detached or nondetached
nature. Sala w i thou t corner houses and each s idehouse
is compl ete in
sala.
which
A sala
all respects of
whose perimeter
its parts in the bhinna
is of ketu yoni and in
the corner houses are differentiated by the
joinings of the exterior and interior beams is called
an abhinna sala.
12
A s~la having four side-houses without common
portions and each
of gamana, width,
prescribed paduka
having the prescribed characteristics
yoni etc, upto the patramana and having
all around, without corner houses is
known as bh inna sala. These salas are suitable to all
especially suitable
are not def ined in
to brahmanas
them. Here
since
the
the corner-houses
perimeter of the
ankana must be of k~tu y5ni and this defines the
characteristics of visuddhabhinna sala.
181
13
The sal as on the southern and western sides are
relatives.
relatives.
Similarly the eastern and northern sal as are
So they may be combined together by adjoining
the corner-house in between them. The other two corners
should not be joined. This portion may be used as a
passway for wommen after delivery, sudras etc.
14
one, two or three corner-houses to
the
By adj oin ing
side-houses, the sala becomes SI i.;;1;a bhinna. Even
though it is
all castes
prescribed
because of
(detached and attached).
for brahmaI')a,
its bhinna
15
it is suitable to
and mi~sra nature
The rear ends of the beams of the side-houses are
to be joined with ends of the beams of ther corner houses
just like the arrangements of petals in the flower of
Nantyarva1;t a , arranged in the anticlockwise direction
in order. Here the perimeter of the ankanattara
(per imeter along the inner beams) must be of ketu yOn i.
It will be auspicious if the perimeter of the paryanta
182
(outer beams) too is of ketu yon i . This sala is known
as Sam~li~~a bhinna sala.
16
It is stated that, in all salas, the yoni of the
corner-houses must be the same as that of the
corresponding side-house. It is known that the corner-
houses are janyas (products) and the correspond ing s ide-
houses are janakas (producer). Therefore in human
houses, Ketu yoni for I~a corner, Simha y~ni for Agni
corner, Vr~a yoni for Nirrti corner and Gaja yani for
Vayu corner are to be obtained accordingly.
17
All the beams of the s~la are determined properly
as in the case of samsli~~a bhinna sala. Then the
per imeters of the corner-houses are so determined to get
the same y6ni as that of their related side-houses. The
joints of the beams of the side-houses and corner-houses
must be made in the left antaralas (intermediary spaces)
of the s ide-hou ses, sI ightly sh i fted from the middl e of
the main door. This is the astasala which is called . SI i~tasala.
183
18
When t he ends of the beams of the side-house and
corner-house are placed very close wi thout joining them
firmly, the sala wi 11 be of bh inna nature.
types of bhinna salas are told in this way.
19
If the lengths of the beams are not
Thus four
sufficient
for the length and width of the sala then they may be
increased upto to the ends of the corner-houses by
join ing the beams according to the rules of joints
prescribed for each sala. The joints of the beams at
the 4 corners are done in such a way tha t the ex ternal
beams on the east and west sides form the adharam and
the other two on south and north sides become the
adheyam.
20
In misrabhinna sala, the perimeters of the
paryanta and ankaI)a are assumed to be of k~tu yoni and
the corner-houses are wi thou t inter ior beams. The beams
of ankal')a are joint at the corners according to the same
norms which are defined for the paryanta (external
184
beams) • All the 4 side-houses must be with their
respective characteristics of y~ni, gati etc.
is a catussala which is the misrabhinna sala.
21
This sala
Since the beams of all the houses are
inter-connected at the corners I th is sala wi 11 have the
mixed characteristics. Since the corner-houses are not
there and the side-houses
characteristics such as yon i I
the qualities of bhinna sala.
22
satisfy their
gati etc, this
respective
sala has
The perimeter of the paryanta must be of ketu
yoni. The
patramanas I
perimeters of
the per imeter
the
of
external and
the ankal)a,
internal
exterior
per imeters of the side-houses and the inter ior per imeters
of the corner-houses must be of ketu yoni. In this
sammisra bh inna sal a, the width of the beam (u t tara) is
to be determined using ingenuity.
23
The perimeter of the ankal)a is to be subtracted
from the desired perimeter of the paryanta. From the
185
remainder subtract 8 times of the length of the interior
side of a rectangular corner-house. Then the width of
the beam is to be determined by 1/16 of its remainder.
The external and internal beams are to be ex tended upto
the paryanta and they are to be joined on four sides.
24
As in the case of sammi~ra bhinna sala, the
internal patramana of the sala must be of k~tu yOni.
Similarly, the external patramana and the inner perimeter
of the corner-house also must be of ketu y5n i. The side
houses may occur with their respective yoni and gati.
This s~na is recommended for Kings (Royal famil ies) and
is called Misraka Cattussala. Since the side-houses are
having their respective YOnis, they are suitable for all
classes. But these s~las are not so perfect for
Brahman~s •
The ankal)a of
and width (square).
beams and patram3nas
25
a sala is def ined by equal leng th
The inner and ou ter per imeters of
(padukas) must be of k~tu ybni.
The perimeters of openings in the middle of these houses,
186
without gati (shift), also must be of ketu yoni.
sAla prescribed for Kings, is called Caturassala.
26
This
If in a ca tussala, the per imeters of all hou ses
are measured along the central line of the beams then
it is called a Maddhyapraru9a sala.
27
If we propose to construct only a single house
then it must be the south house. If there are two houses
then they must be t he sou th and wes t houses. When three
houses are to be constructed I the north house is to be
adjoined to the above two houses. If four houses are
needed the above three houses together with the east
house is . to be constructed. In some cases, west house
is accepted instead of south house for a single house.
In the construction of sala having more than one house,
the order of construction must be as given above.
28
I f there are three houses in a sala wi thout the
east house then it is called I Suk~etram I which prov ides
187
prosperi ty to the owner of the house. The sala without
the south house is called 'Culli' and this causes
destruct ion of weal th. The sala comprising of 3 houses
without the west house is named 'Dhvam!3am I which causes
destruction of son and difficulties from enemy. If there
are three houses excluding the north house, it is called
'Hirannyan~bhi'. This will always provide wealth.
29
When the two houses are constructed without the
east and west houses, it is called 'Kaca ' . This will
prov ide quarrel and fear. If the other two, namely, the
east and west houses are constructed without the south
and north houses then it is called 'Siddharthakam'. This
will generate weal th and fortune. It is told that if
two houses are del eted, in ord er, from east side onwards
then they will provide death, fear, quarrel, and wealth
respectively.
Chapter V
1
The region selected for the construction of house
is to be raised to a height of 8, 12 or 16 angulas with
earth, stone etc, in order to avoid the d i ff icu 1 ties due
to the dip at the cen t ral cou rtyard for water to ooz e
188
out from the inner and outer ankaoas (yards).
2
In all buildings an upapr~ha of width one or two
hastas is to be constructed below the adhi~tana for
strength, beauty and height of the building. A
Kuzhi yankaJ;lam (cen t ral courtyard) of KIHhu yon i or Vrsa
yOni with South-North elongation is to be constructed
inside the house. Then a water-let is arranged in the
lsa-corner with its opening towards the north or east
direction.
3
The height of the upapitha in a house for man may
be equal to that of the height of the adhi~~ana or one
part less than this when it is divided into 6, 7, 8, 9
or 10 parts as requ ired. The paduka, jagat i etc, are
to be constructed by dividing their respective heights
accord ing ly.
4
A square is determined in the middle of the
KuzhiyankaQam (central courtyard) by deleting equal
189
lengths
length
(which is equal to half of the difference between
and width of the ankat;la) at the south and north
ends of the ankat;la. Then the square is div ided into 64
cells (padas). The Mullathara (the place for growing
jasmine) may be constructed at the southern side in the
Apa pada or at the northern side in the Apavalsa pada
in the middle envelope of cells.
t
5
Mulla thara may be in the shape of square, octagon,
sixteen-gon or circle and must be of ketu yon i. It may
be constructed with upapi tham and such other parts, with
decorations of Kumuda, pattam etc, on it. Its height
may be determined as the height of the adhistana of the
house or one part less than when it is divided into 6
to 11 parts as required. Thus the Mullathara is defined
without its vedha (intersection or coincidence) wi th the
rajju (diagonal).
6
The lCherippu 1 (upanaham) of the adhi~~:€ma is
be done strongly upto the level of upapItha. Paduka
to be constructed above the upapitha on all sides
to
is
of
190
adhistana. All other parts on adhist~na are to be
constructed accordingly upto the level of patramana as
prescribed earlier.
7
The onward projection of the adhi~tana from the
foot of the perpendicular from the outer-edge of the beam
(uttaram) is def ined as the Pat ramana. The outward
projection may
times of it
projection on
be taken as 8 angulas or two times or 3
as required. As
south side and north
6 angulas and an outward projection
a special case the
side may be taken as
of 12 angulas on the
west side is acceptable in some cases.
8
In houses the inner and outer patramanas may be
of the same or different widths. They are determined
in such a way that they satisfy their respective yonis.
In temples the patramanas of the dipamala (vilakkumadam)
in antahara and the g6pura (entrance) are determined in
the same manner.
191
9
According to scholars, the region outside the
padukas of the four houses (central courtyard) is called
'prankar;ta I • This have elongation in South-North
direct ion and in the form of a rectang 1 e. The length
may be larger than the width by 1, 2, 4, 8, 9, 12 or 16
angulas or this may be greater than the width by I, 2,
or 3 hastas. Otherwise, the length may be determined
by the gunam/sa method. In any case, the perimeter may
be of the Ketu yoni.
10
If the central lines of the ankaQa (courtyard)
and the four side-houses (diksalas) intersect then the
residents will suffer from several calamities to their
children. Therefore the centres of the houses are to
be shifted in the clockwise direction. These shifts from
the east-house onwards are 3, 9, 7, and 5 angulas
respect i vely so that they prov ide the yon i corresponding
to each side. I f the sh i fts are to be small, the gamanas
(shifts) may be done using yavas instead of angulas.
When 8, 16,
respective angulas of
192
11
or 24
shifts
angulas are
of four-side
added to the
houses, their
respect i ve yon is wi 11 be the same. Therefore, in houses
where the intermediary spaces (antar~las) are small, the
increased shifts are to be accepted.
12
To distinguish between the side-houses and the
corner-houses there will be eight antar~las. I f the
antariUa is too large, the resu 1 t wi 11 be loss of weal th.
If it is too small, illness wi 11 be the resul t. When
the walls coincide, there will be no space between them
and the result will be death. Therefore it is not
auspicious to have antarCilas greater than 1/6 the length
of the house or less than it by more than 2 or 3 angulas.
13
The inner width between the respective beams and
cerippu is known as the p~dam~na. In small houses it
is seemed to be 3~ hastas. According to great acaryas
the padamana is to be equal to the width of the house
or 1 ~ t i m e s 0 fit . It may also be determined by add ing
or subtracting one part of width to or from it when it
193
is divided into 4, 6, 7, 8, 9, 10 equal parts.
14
When this padamana is divided into 3, 4, 5, 6,
7, 8, 9 or 10 equal parts, the measure of one part wi 11
be the height of the addhistana. .. I fit is d i vi d ed in t 0
21 parts, the measure of 6 parts will be the height of
the adh i~ ~ana. Further, when it is divided into 18, 24
or 7 parts, the measure of 5, 7, or 2 parts respectively
will be the height of the adhi~tana. Similarly, when
it is divided into 15 or 14 parts, the measure of 4 parts
is the height of the adhi~~ana.
15
As explained above, the heights of the adhi&1;ana
are def i ned in 14 ways. By subtracting one part each
from their respective heights when they are divided into
6, 7, 8, 9, 10, or 11 parts, the height of the adhi~tana
will occur in 84 ways.
16
When the chosen height of the adhi~~ana is divided
into 9 parts, the height of the paduka and jagati are
194
determined by 3 parts and
may also be done by taking
6 parts respectively. This
the measures as paduka by 2
parts and
two types
jagati by 7 parts in
of mancakas (adhi~~ana)
order. Thus there are
without pati and gala.
The proj ecti on of the padu ka from the edge of j agat i may
be determined as 3/4, 1/2 or 1/3 of the height of the
paduka or it may be defined by 3 parts when the height
is divided into 5 parts.
17
When the desired height of the adhi.!?tana is
d i v ided in to 6 part s, the heigh ts of the paduka, j aga t i,
gala and pa t i are to be determ ined on the mancaka by 1
part, 3 parts, 1 part and 1 part respectively.
When the height of
5 parts, the he igh t of
part. The
determined by
heights of
2 parts, 1
18
the adhi.!?~ana is divided into
the paduka is determined by 1
jagati, gala and prati are
part and 1 part respectively.
Mancaka may be constructed also by this method.
195
19
When the height of the adhistana is divided into .. 14 parts, the paduka is to be constructed by 2 parts.
The heights of jagati, the lower vajana, an ornamentation
of the gala, gala, upper vajana galamancaka with vajana
and is very prosperous.
20
Thus the gal amancaka are def ined in 3 ways. The
shift of the pati will be equal to that of jagati. In
these galamancakas the inward shift of gala will be ~
of the height of the gala.
21
In this way the adhi~tana (basement) is
constructed strongly. Then the height of the pillar
(stambha) is defined as the difference between the
padamana and the height of the adhi~~ana. The height
of the pillar may be defined by adding or subtracting
one part to or from it when it is divided into 6, 7, 8,
9, 10 or 11 parts. From this height (length) of the
pillar, the height of the p~dapee9am (pedestal) (5ma)
and the thickness of the potika (bracket) are to be
subtracted.
196
22
The pedestal (oma) must be made of strong stone
or by the core of strong timber. This may be done in
the shape of square, octag one, or sixteen-sides and in
some case this may be done l.n circular shape. The width
of the pedestal must be the length of the diagonal of
the foot of the pillar and the height must be half of
it. This height may be reduced by 1/4, 1/3, or 1/2 of
it. In some cases, this is done l.n the shape of a lotus
flower together with ornamentations like vajana etc. The
pedestal (Bma) is to be placed above the adhi~tana.
23
All pillars must have rectangular projection at
their ends with a width of 1/3 of the width of the
pillar. These pillars are placed on the pedestal placed
at their respective positions in such a way that the
projections (kutuma) at their ends are exactly inserted
into the holes on the pedestals (Oma).
24
The breadth of the foot of the pillar is
determined by one part of the height of the pi 11 ar when
197
it is divided into 4, 5, 6, 7, 8, 9, 10 or 11 parts.
The width of its upper end is given by 1 part less than
the width of its lower end when it is divided into 8,
9, 10 or 11 parts. The width of the upper end is known
as a da~~u. In some cases th is dandu is used as a un i t
of measurement. This daQqu is used for measuring the
ornamentations on the walls. The width of the upper end
of the pillar on wall is also known as daryqu.
25
On all pillars a rectangular block is to be
constructed at the upper end whose length is equal to
the length of the diagonal of the foot of the pillar.
At the lower end the rectangular block will have length
equal to 3~, 4, 5 or 6 times of the length of the
diagonal. In the middle of the pillar there must be a
rectangular block of length equal to the length of the
diagonal of the pillar at the middle. The rema in ing
parts may be done in the shape of octagon (ettuoattam).
Otherwise, the whole portion of the pillar may be done
in the shape of circle, octagon or sixteen-side (:;;odha/sa
pattom).
198
26
The three types of pillars in the shapes of
circle, octagon and sixteen-sides are to be done with
their lower half in rectangular shape or with a
rectangular block at their lower ends having length equal
to the length of the diagonal of the foot of the pillar.
27
When the pillar is too tall, its breadth is to
be taken as l~, l~ or 2 times of the respective pillar
which is def ined above. The breadth is to be increased
upto the middle of the pillar or upt 0 a height of the
adhistana or l~ times of the height of the adh istana . . . In this way, the pillar is to be constructed with granite
or fr ied br icks using the prescr ibed quant i ty of I cunna I •
In some cases this is to be done from top to bottom or
upto the middle of the pillar.
28
If there is only one vajana on the beam the
rectangular block in the middle of the pillar is avoided.
In the case of patrottara or beam with a small vajana,
the rectangular block at the middle is auspicious. On
199
pillars wh i ch are meet ing the pa trot ta ra and vaj anottara,
ornamentations of muthupatta, kuzhitara, valaya etc, are
to be constructed. All parts of the house below and
above the beam (uttara) are to be done according to the
nature of the main beam.
29
The width of the potika is the average of the
widths of the beam and the upper end of the pillar or
it may be the width of the pillar at the middle. The
thickness of the potika will be half of its width. The
length of the potika is equal to 3 daf)9 u , 4 dar;tqu or 5
dar;9u or it may be equal to 3 times of its width. The
potika may be decorated with vajana and such other
ornamen tat ions and is to pI aced on the Roop<'5thara of the
house.
30
If the beam is a patrottara the above mentioned
potika must have thickness equal to 3/4 of its width.
If it is a khand6ttara the thickness must be equal to
its width. All parts, at all situations, are to be done
beautifully.
200
31
The appropriate width of the beam is to be
determined according as the rules def ined for the
determination
The width may
The
of the
also
beam
width of the
be determined
foot
by
of
8,
the pillar.
16, 12 or 6
angu1as.
called khandottara
with
and is
equal width and thickness is
auspicious. The beam hav ing
thickness 3/4 of its width is known as Patrottara and
considered madhyama and when the thickness is half of
its width is named as Roopottara and is adhama.
32
In some cases, the width and thickness of the beam
may be done in the reverse order. Such beam is known
as chilli (choozhika). Since it is in an inclined
position, the rafters are fixed on it directly.
33
If there is only one vajana on a beam then it is
divided into 5 parts. The upper patta is to be done by
2 parts and the lower patta by the remaining 3 parts.
34
If there is the alpavajanam also on a beam then
201
the mahavajanam (small vajanam) by 1 part and the
remaining 4 parts will constitute the lower pat tarn when
the thickness of the beam is d i v ided into 8 equal parts.
(The inward proj ect ion of the mahavaj ana and al!Javaj ana
is to be done by 1 part.)
35
When the thickness of the beams are divided into
5 parts, the mahavajana is to be done by 2 parts, the
small vajana by 1 part and the pattam is to be done by
the remaining parts beautifully. If the thickness of
the beam is divided into 4 to 11 parts, the shift of the
two vajanas is to be done by 1 part, accordingly. In
all other cases, the rules for vajana are the same.
36
Then the potika is to be placed on the top of the
pillar. The upper end of the pillar projects upward
through the hole on the potika. The beam is placed on
this p~tika and is fixed on the protruding end of the
pillar.
37
Then an uttarappattika known as Chittuttaram of
height equal to the thickness of the beam and thickness
202
of half it is to be pI aced over the beam and is fix ed
to it using appropriate wooden pegs.
38
These wooden pegs are to be fixed in the middle
of houses and in koota sut ras • All these pegs are to
be fixed by shifting them from the central areas by one
yava towards the right side. The gap between the rafters
on the beam are to be determined intelligently. These
pegs are to be fixed in the middle of the interspaces
between the rafters so that the number of pegs will be
odd and the number of rafters will be even on each side.
39
A vaj ana-beam hav ing thickness 3/4 daQQu or more
is to be placed on the main beam. On this vajana-beam,
beams with height I dandu .. and thickness 3/4 d-andu are
to be arranged in the crosswise direct ion on them, shor t
beams (Jayantis) having thickness equal to half the
height of the beam are to be arranged according to the
nature of the roof of the house. The upper side of the
beams is uniformly levelled and wooden bands of
appropriate thickness are fixed on it without gaps.
203
40
Or the ceiling is to be done magnificiently with
decoration like kap~tam, valaru, tulapadam, uruvu, net ram
etc. Beauti ful pictures and statues of d i ff erent dei ties
may be engraved on the cei 1 ing board to make it art ist ic.
In the case of
is sufficient. The
Chapter VI
1
small houses, only
Arudam (secondary
the outer-beam
beam) , is also
necessary if the house is big. The arudam is to be
placed upon the vi~kambham (etavattom) with an inward
shift of 8 angulas, 16 angulas, 24 angulas etc, from the
outer-beam (var6ttaram) so that it satisfies the y6ni,
aya etc, prescr ibed for the house. The height of the
Aru<;1am from the level of varot tara is equal to the sh i ft
of the Kru9am and the 1 ength of its support is equal to
the hypotenuse of the isosceles right angled triangle
formed by the height. The intermediary space between
the ~ru9am and the Varottaram is known as the ali~qa.
2
The support of the Vi~kambam is to be done
beautifully with special decorations like chippam etc,
204
together wi th v ine on it bear ing f lowers and buds
appearing to be emerging out from it (chippam).
3
The
determined
dip of
by 2/5,
the rafters (kazhukkol chattam) is
4/9, 3/8, 3/7, 1/3 or 1/2 of the
length of the pillar.
accordingly.
Anyone of these may be adopted
4
Di v ide the height of the pi lIar below the 1 evel
of the prescr ibed dip of the rafter into 6 to 11 parts.
Subtract or add one part from or to the dip as
prescribed in the case of determine the height of the
pillar. In some cases, this may be done by subtract ing
1, 2, 3, 4, 5, 6, or 7 angulas. The dip may be done on
either side of the house as equal or unequal.
5
The dip of the rafter may be determined by I, 1%,
2, 3, 4, 5, 6, or 7 times of the width or thickness of
the uttaram (beam). When the house annexed to other
houses, the dimensions of the rafters, vamata, fillet
205
etc, may be reduced accordingly. Uttara (beam) is the
most important part of a house and therefore it should
not be cut into pieces.
6
Rafters which are straight and having the same
lengths and widths are known as 'nermanju' (common
rafter) • Rafters
placed in sI ant ing
and upakot i ( jack
having different lengths
positions are called koti
rafter) . All the rafters
and widths
(hiprafter)
on either
sides of the house must be of the same dimensions.
7
One end of the hiprafters, jackrafters etc, are
to be fixed on the kllta and the straight rafters (common
rafters) are to be fixed on the 'montaya' (Ridge). The
other ends are to be placed on the C i t tu t tara properly.
8
Since the rafters on either sides of the ridge
are fixed on the mon taya ( ridge), it is called Vamsa.
The th ickness and width of the ridge may be equal to 3/4
of the width of the uttara or they may be determined by
6 or 7 angulas. A t the pos i t ions of the rafters, the
206
patra and vajana are to be made wi th a measure of 3 or
4 times of the thickness of the rafter.
9
The kutam is fixed on the pivot at the end of the
the sides are to be fixed hipraf ters. The rafters on
on the kutam using
at the end of the
iron nails at their ends. The pivot
rafter is the basis of the kilta and
therefore the base of the kuta must be on the lower side.
In the case of square houses all the rafters will be jack
rafters or slant-rafters (Alasi).
10
The kOtam is to be done in the shape of a
'Durdura' flower (Thorn-apple flower) or in a cylindrical
shape, or polygon of 8 sides or 16 sides. This may be
constructed in the shape full-blossomed lotus flower.
The lower half must be in spher ical shape and its length
will be double the width. Its length may be reduced by
1 part when it is divided into 8 to 11 equal parts in
order. Its middle portion is to be decorated by
constructing 'patras' having width of 4 yavas or more.
207
11
The perimeter of the kuta will be approximately
equal to the total i ty of the th icknesses of all rafters
or may be equal to the wid th of the ut tara. This may
be determined in the un it of angula in order to sui t the
prescribed yoni conditions. The pattam where the rafters
meet the kuta must be of height equal to the line of
vitana of the hip-rafter. Kutam is an upward directed
element of a house and is decorated wi th special features
of Patra. The shape and dimensions of the kuta are said
to be as above.
12
In rectangular houses having length greater than
the width, the rafters like k6ti, upak15ti etc, are to
be fixed on the kuta which is fixed on the ridge of the
house. Other straight rafters are to be fixed on the
vamsa (ridge) using iron nails at the ends.
13
If the pivots at the ends of the ridge are screwed
into the hol es on the s ides of the kuta then th i s joint
is named 'Ajayudha sandhi'. Here also, depending on the
208
nature of the join t I the base of ku ta must be on the
lower side.
14
In houses (rectangular) with side elongation
(Mukhiylma) the length of the ridge must be equal to that
of the uttara (beam) of the house. The rules regarding
the joins at the ends of the beams will be the same as
those prescribed for the houses.
15
The pivots at the two ends of the ridge are
inserted into the holes on the lower portion of the kutas
and are to be fixed on it us ing wooden na il s. Since the
kuta depends on the mon taya (r idge) lit wi 11 be in the
ups ide down posi t ion. In the same way, the b~l akutam
also depends on the element above it.
16
In all desired squares, the side below in the
crosswise direction (horizontal direction) is known as
'bhuja' (base). The line through the corners is the
diagonal (kar~a).
209
17
On a smooth wooden board or on smooth ground
construct a square wi th its s id e eq u a 1 to ha 1 f the w i d t h
lines parallel to the bhuja of the house. Draw
represent ing the height of the c i t tu t taram, the th ickness
of the uttara and the dip of the rafters in descending
order. Determine the positions of the rafters on the
line representing the uttara.
Double
slantrafter,
this number
between the
18
the number of
jackrafter etc,
in all cases.
rafters like hiprafter,
and then subtract one from
The intermediary spaces
koti, upakoti, and slant rafter are
determined by two parts each and one part near to the
vertical side of the square. This kind of representation
of the positions of the rafters are recommented by all
s§stras.
19
In this way the positions of the slant rafters
are determined on the line of beam. Then the lines
through these points joining the kGta and dip-line will
determine lengths of the corresponding rafters.
210
20
In all houses the width of the straight rafter
(common rafter) wi 11 be equal to the width of the ut tara
(beam) or it may be determined by adding or subtracting
1/8, 1/7, 1/6, 1/5, 1/4, or 1/3 of width to or from it.
3 1 Or it may be done by 2, 1-, or 1- times of the width of
4 2
the uttara. The thickness of the rafter may be
determined by 1 angula to 6 angula, each time increased
by 1 yava successively.
21
Consider a square wi th side as the width of the
common rafter (Manju). Mark a point on the bhuja
representing half the length of the diagonal of the
square. The line joining this point and the terminal
end of the koti (vertical side) will give the width of
the h iprafter. The widths of each of the slant-rafters
is given by the 1 engths of the 1 ines join ing the upper
end of the koti and the corresponding positions of the
slantrafters on the bhuja. On either sides of the
rafters three lines like dwaja 1 ine etc, and plumb 1 ine
etc, are to be constructed.
211
22
Di v ide the width of the rafter int 0 9 parts and
the dwaja sutra is to be drawn 1n the middle of the
rafter on both sides such that 5 parts are above and the
remaining 4 parts are below the dwaja sutra. Or this
may be drawn in such a way that 4 parts are on the upper
side and 3 parts are on the lower side of this 1 ine.
It may also be determined such that 3 parts are above
it and 2 parts are below it when the width is divided
into 5 parts.
23
On ei ther side of the dwaja sutra (1 ine) draw two
lines parallel to it at a distance of 2 angula from it.
The widths of the rafter below and above these lines are
to be determined properly.
24
On both sides of all rafters construct squares
of sides 4 angul a on the dwaj a sUtra. The diagonals of
the square are known as vert ical 1 ine (Tu ku rekha) and
horizontal line (vitana). These lines are to be drawn
at the positions where the vala (collarpin), the beam,
212
the ridge etc, meet the rafter. They are to be
constructed at the ends of the rafters where the rafters
meet the kata and vamata.
Chapter VII
1
In the case of small houses, Cuzhika (slant beam)
may be used in the construction of roof. Bu t v iskarhbam ,
(vittam) must be In even number. The ridge IS to be
placed on the pillar of length equal to the semiwidth
of the house. The pillar is placed at the centre of the
vittam. The length of the pillar may be reduced by 1/7,
1/8, 1/9, 1/10 or 1/11 of its length. The rafters are
to be placed on the Cuzhika (slant beam) with their other
ends on the prescribed ridge.
2
The width of the vamata is determined by 6/10,
7/10, 8/10 or 9/10 of the width of the beam. Or it may
be def ined by 3/4 or 3/7 of the width of the beam. Its
thickness is 1/3 of its width. It may also be determined
by 2/5 of its width.
213
3
If the width of the vamata is divided into 5 parts
then the upper pattam is done by 2 parts, the talam by
2 parts and the lower pattam is done by 1 part.
Similarly, when it is divided into 6 parts then the upper
pattam is done by 2 parts, the talam by 3 parts and the
lower pat tarn by 1 part. I f the width of the vama ta is
divided into 8 parts then the above parts may be done
by 3 parts, 4 parts and 1 part respectively.
4
Divide the width of the vamata at the paryanta
(Tumbu vilmata) into 5, 7 or 9 parts. On all sides, the
level of the varnata along the vi tana is to be ra ised by
3 parts according to the rule of koti-karrna and is fixed
at the ends of the rafters. A light wooden board known
as 'tuvanapalaka' is to get fixed along the edge of the
v3mata by the expert craftrnan. This is to be done
carefully after performing Vayavya-homa.
5
The vala (collarpin) is to be done in square shape
wi th th i ckness from 14 yavas to 3 angulas increas ing by
214
2 yavas at a time. The th ickness of vala is def ined in
6 ways by the sages. Of these, the appropriate thickness
may be accepted depending on the width of rafters.
6
The width of the pattika (reapers) is determined
by 17 yavas and its thickness is the measure of 9 yavas.
The space between the pat t i kas (reapers) is 63/4 of its
thickness and these are to be fixed on the rafters using
iron nails.
7
In all houses, for cover ing the roof using t i 1 es
the pattika (reapers) is to be fixed on rafters as
prescribed above. In some cases, thick wooden boards
are used instead of pat t i ka and fixed on the roof wit h
nails. On these wooden boards sufficient grooves are made
in order to fix the tiles on them properly. In the case
of templ es, palaces etc, if copper pI a tes are used for
thatching, to protect from heavy rainfall, then there
is no need of groove on them.
8
The turban of the Grhapuru~a is known as the
Apidh~nam (end). I t is to be placed ups ide down on the
roof.
of the
The width
height of
215
of the Apidharl~m
the foundat ion
equal to the height of the paduka.
9
is to be 1/2 or 3/4
and its thickness is
The doors (openings) to the ankaDa are to be
placed in
wi th the
such a way that their central line coincide
centre of the
of the houses and ankaJ;la.
space between the
Their perimeters
central axes
in terms of
angulas must be auspicious with respect to yoni, aya,
vyaya etc, prescr ibed for each side from east onwards.
The width of the door-frame will be equal to that of the
beam and the th i ckness will be equal to or half of its
width or I part less than the width when it is divided
into 3 or 4 parts. On the door-frames decorations of
vajana etc, are to be constructed properly. There must
be 'patis' at the lower and upper ends of the frame.
10
The lower pati (Cettupati) of the door will have
thickness I part greater then the thickness of the frame
when it is divided into 3 or 4 parts and without
decorations of vajana. The thickness of the upper-pati
(Kurumpati) must be the same as that of the thickness
216
of the frame. The upper ends
be extended to meet the beam
of the door-frame are to
placed above them. The
inner-perimeter of the door must have the respective
yoni, aya etc, prescribed for each side. The width of
the door is
length from
to be determined by subtracting the desired
the semiperimeter or by gunamsa method
(Multiple division method).
11
Then the 'Kurumbappalaka' is to be placed upon
the upperpati (Kurumpati) of the door. It is decorated
with the images of Gan~sa, SrIkrishna, Mahalakshmi and
such others together with pictures of different birds
carved on it beautifully according to the situations.
12
If the wall is too thick then it is divided into
12 parts and consider the line which separates the parts
into 7 parts ins ide and 5 parts ou ts ide of it. The door
frame is to be placed wi th its cent ral line coinc id ing
wi th the above line. In some cases, one more pa ti is
placed upon the upperpati (Kurumpati) and above it wall
is constructed using granite and mortar or mud.
217
13
In houses where the innerperimeter is considered
important and walls of much thickness, they may be
constructed strongly along the outer edge of the paduka
(without the inward shift). The p:)si t ions of door-frame
and beam are to be shifted outward upto the prescribed
limi ts of the wall and pI aced properly accord i ng to the
conditions of axes of houses and ankana.
14
Each of the two shutters of the door is to be
const ructed with its width equal to half the sum of the
width of the door and thickness of the shutter. The
thickness of the shutter may be determined by 2, 2~, 3,
3~ or 4 angulas.
15
There must be pivots (hinges) at the lower and
upper ends of the door. SGtrappattika (Blinding reaper)
and a metal ring for holding the shutter are to be fixed
on the shut ters. Copper or iron strips are to be fixed
on the door both in lengthwise and crosswise using nails
with their nuts in the form of buds and flowers.
Further, the image of the face of Mahalakshmi and part
of moon (Candrakala) may be done 0:1 t he door to make it
beautiful.
218
16
The width and thickness of the sutrappattika
(blinding reaper) are determined by 1 part of the width
of the opening when it is divided into 4 to 8 parts. The
thickness may be fixed as 1/2 or 3/4 of the width of the
sutrappattika. Its length (height) will be equal to the
length of the door. It may be decorated with an odd
number of (3, 5, 7 etc,) projections in the shape of
breasts, images of Ganesa, Sri kr ishna, Mahalakshmi
resting on the lotus flower, muthumala etc, on it.
17
The shutter on the left side of the door is called
the mother and the sGtrappattika is to be fixed on it.
The right side shutter is known as the daughter. The
shutters in all the doors are defined like this. Then
the 'arama' (matiyan) is to be constructed wi th height
equal to 1/3, 1/4, 1/5 or 1/6 of the height of the door
and its width and thickness equal to 1/4, 1/5, 1/6 or
1/7 of its height.
18
The bolts (saksha) are to be made with length
equal to 1/4, 1/5, 1/6. 1/7 or 1/8 of the width of the
2L9
door. Its width is defined as 1/6, 1/7 or 1/8 of its
length and thickness is equal to half of its width. Two
rectangular blocks where projection is equal to the
thickness of the bol t are to be const ructed at the ends
of the bol ts. These bolts are fixed on the arama through
the grooves at their lower and upper ends such that the
rectangular blocks on the bolts will be on either sides
of the arama.
19
The lower bolt (saksha) is to be placed on the
mother-shutter and the upper bolt on the
daughter-shutter. Then the 'arama' (matiyan) is to be
fixed on the inner side of the door using nails with its
cent re is just above the centre of the door.
20
It is considered auspicious to have the
door-frame, shu t ters etc, made of the same kind of
timber. I f they are done by different kinds of timbers
then according to some acaryas I the ladies res iding there
will be of bad character.
220
21
If the door is having only one shutter then it
must be pI aced on the left door-frame. The arama is to
be fixed on the oppos i te frame just below or above its
centre. The bolt of this 'arama' is to be done in
circular, octagonal or rectangular shape.
be fastened using strong chain also.
The door may
22
Divide the length of the house into 11 or 13 parts
by 10 lines and 12 lines respectively. Then the outward
door is to be placed in such a way that its centre
coincides wi th the 6 th or 7 th 1 ine on the r igh t side of
the house. This is to be done in accordance wi th thei r
appropriate yoni, aya etc, prescribed for each house.
If there is only one shutter then it must be fixed on
the left side with respect to the exit of the house.
23
The main door which is used for the transportation
between the ankana and outside is to be placed upon the
paduka. I f the corner-house has wall then the width of
the an tarala (al inda) is to be so chosen tha t when it
is multiplied by 4 gives a perimeter of appropriate yoni.
221
24
The patippuras (g6puras) or the large entrances
to the house are to be done at the positions of
Pu~padanta, Ballata, Indra and Grahakshata at a distance
of 4, 5, 6 or 7 dandus from the centre of the ankaJ;la.
These large entrances and eight other small entrances
may be constructed at positions where the region is
higher than the surroundings. These patippuras may be
done with upstairs together with projection on it.
25
The padas (positions) of eight
(gate-house) are defined for houses of
at the padas of Pa'rjanya I Bruin'Sa I
Dvarapala, So~an, Naga and Aditi.
26
small patippuras
man. They are
Pu:;;avu,
The vedika for sitting is to be constructed, on
both s ides of the entrance, above the f oundat ion of the
gopura. The height of the v~dika may be determined by
the width of the pillar at the entrance or by 1/6, 1/7
or 1/8 of the height of the pillar or by the height of
the pati or by l~, 2, or 3 times of it. Upon the vedika
222
there must be pi lIars in even number and on ei ther side
walls are constructed with beams on it. The width of
the beam may be equal to the width of the pillar or it
may be equal to half or 3/4 of it.
27
The requ i red shift in the position of vedika may
be incorporated in accordance with the order of
patram~na • The shift of the vedika from the edge of
uttara is defined by 2~, 3 angulas etc, in order.
28
According to some scholars, vedika lS to be done
using the same materials which are used to construct the
wall and foundat ion of the house. In all houses, it is
seen that, the ved ika is don e by material s like stone,
fried bricks, mud etc, or by different kinds of timber.
As in the case of garbhagrha, when the yoni is determined
wi th respec t to the inner per imeter, the door-frame is
to be placed upon the ankaQa-paduka or below the patio
29
The number of pi llars below the beam, rafters etc,
must be of even number and the number of interspaces
223
(gaps) between them must be of odd number. It wi 11 be
inauspicious if the lengths of interspaces exceed 1 kol
(hasta) and it will provide calamities.
30
The east-house is prescribed for Puja, sacrifice
etc, and the north-house is def ined for family members.
These two may be interchanged. The south-house is
utilised for reception of guests and the west-house is
used for st orage of weal th. These may be used in the
reverse order. The remaining spaces of these two may
be used for sleep and study.
31
The region is divided into 100 padas, 81 padas
or 64 padas
compr is ing of
(squares) .
16 padas
will form the ankana.
Then the por t ion at the centre
9 padas or 4 padas
The surrounding two
respectively
envelopes of
padas will be the space for the construction of houses.
The outermost envelope prov ide the space for cattle-shed,
kalappura, well etc.
The Kalappura
southern side and the
224
32
(barn house)
grain-house may
will be done on
be constructed on
the southern side or in the Nirrti corner. Then the
treasury-house may be built on north, east, or west side
or at the signs of Simha, Vrscika, Tula or Karkilaka and
at all positions which are defined for the grain house.
If necessary, the grain-house may be constructed at all
positions which are prescribed for the wealth house.
33
'Gosala' (cow-shed) may be constructed at the
positions of Indra,
Vitatha and pu~avu.
VaruQa and in the antaralas of
It may be done at the pad as of
parjanya and jayanta and in the anter~las of kusumadanta
and dvarapala. I n the case of the Mahi~al aya, it may
be done at the positions of BFunga and 50:;;a or on the
south side. The ox-shed must be made on the sout h side.
In all these constructions the vastumarmas and sulas are
to be avoided.
34
Some acaryas are of the v iew that on all sides,
the passage for cows across the karrya so. t ra (raj ju) is
225
not auspicious. For cowsheds, vrsa yoni is the most
auspicious and Simha yoni is inauspicious. The Karanas
of Simha, Puli, ~unaka (dog), Gardabha (ass) etc, are
to be avoided in the construction of cowsheds.
35
Kitchen is prescribed at the padas of Parjanya
and Agni or it may be at the signs of Mesha, and Etava
or at the vayu corner. Dining hall is wished to be at
these positions itself or at the sign of Makara and on
west side also. The house for entertainment lS to be
constructed at the signs of Kumba and Makara and at the
Vayu corner. If necessary, this may be done at the signs
of Etava and Mesha. S imi larly, the gr ind ing house is
to be done at the v~yu corner.
36
Well at the Meena sign (rasi) is defined to be
the most auspicious. This will increase wealth in all
ways. Well at the signs of Mesha and Kumba will provide
prosperity and at the signs of Makara and Etava will
prov ide immense weal th. I t is auspic ious at the pad as
of Apa and Apatvalsa.
of Indrajit also.
It may be constructed at the pada
Well on west side is auspicious
whereas at the V~yu corner is not good for women.
226
37
Well at the Antarlk~apada is prosperous.
Similarly, a lake is
Mahidhasu, and Varu~a,
at the sign of Mesha.
def ined at the padas of Mahendra,
on the sides of S6ma and Siva and
I t is seen that the 1 ake is done
at Vayu corner or Ni r~t i corner. I t is not auspi c i ous
to use the water from the same tank for bathing and
drinking. Therefore, if there is no river passing by
them water for bathing and drinking is to be collected
separately.
38
If the construction of well and similarly, of lake
have
they
been
will
completed prev iously at
cause difficulties from
the Agn i corner,
fire etc. The
then
tank
on the south side will also provide the same results.
Some acaryas consider
'dIrghika' etc, on
( v i 11 ag e ) et c • I n a
holes of snakes etc,
it inauspicious to have lake like
the southern side of the gramas
similar way, the presence of park,
in the immed ia te vi cin i ty of the
houses are not auspicious.
39
In the houses of Kings and Brahmaoas, the house
227
for daily worship is to be done in the anka~a and the
install a ti on of the d harmad~va (dei ty of the f ami 1 y) etc,
are to be done at the positions of rsa, Indra, Agni and
VaruIJa. The buildings like temple etc, at the positions
of Isa, Indra, Agni and Yama are to be done with
perimeters of K~tu y~ni and from Nirrti to Isa corner
they are to be done in Vrsa yoni for prosperity.
40
The temples of family-kuladevatas are to be done
with Ketu yOni from Isa corner onwards and with VF~a yoni
from Nirrti corner onwards. They must be faced towards
the positions of houses, puram, pattar;tam, nagaram, grama
etc.
41
Images of deities may be installed in some houses
wi thou t the pres cr i bed combina t ion of its parts. There
are two types of dei ties, namely, temporary and permanent
depending on their varying and nonvarying nature and on
the nature of offerings made to them.
42
For Kings, the chamber for enjoyment is to be done
at the Mitra pada and the house for entertainment is to
228
be constructed at the Vayu corner. The house for
exercise is made at the Arggala pada and at the Nirrti
corner. Bathrooms and such others are constructed at
Parjanya pada and dining hall is to be done at Indra pada
and Varupa pada. Natyasala is to be made at Gandarva
pada and the arsenal must be done at the Nirrti corner.
Chambers for sleeping are to be made at the Grahak~ata
pada and on the east side.
43
It is said to be auspicious to have the compound
wall outside the boundary limit constructed with stone
or mud properly. A trench along this limit is considered
Madhyama and a fence using the branches of trees is
adhama. For making the fence branches of thorn-trees,
vines, bamboo etc, may be used. Anyone of these may
be accepted depending on the wealth conditions. Then
the trees prescribed for each side are to be pI an t ed in
order as explained earlier.
44
The acarya has to get the house compl eted by the
artisans according to the above rules and at the end of
its construction the silpins must be awarded with
presentations like bracelets, orQaments with jewels on
them etc, to make them happy. After accepting the house
the acarya together wi th the owner and from the B i lpins,
229
family must
accordingly.
enter the house at an auspicious time
The vastupuja and other offerings are to
be performed as prescribed in this connection.
45
At the end of the offerings, the owner of the
house has to propitiate
presentations like cows,
the acarya by
earth, gold,
awarding him
feasts etc,
according to his satisfaction and after getting his
permission the house-owner must give presentations to
all for making them happy. Then the grhakarta may live
in the house with pleasure and satisfaction.
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BIBLIOGRAPHY
1 ~chl1rya. P. K. (Tr) "Architecture of Ml1nasl1ra", The
Oxford University Press, 1934.
2 Adoor K.K. Ramachandran Nair (Editor), "Gazeteer of
3
India", Kerala State Gazeteer Vol.II, Kerala
Gazeteers, Trivandrum, First Edition, 1986.
Ananda. K.
Indonesian
1972.
Coomaraswamy, "History of
Art" , Munshiram Manoharlal,
Indian and
New Delhi,
4 Andrews. G.E., "Number Theory", Hindustan Publishing
Corporation (INDIA) Delhi, 1984.
5 Balakr ishnanasar i. S, "Thachusastram Bhasha", (Mal) ,
K.U.O.R.I.M. Library, Trivandrum, 1982.
6
7
Banerj~e. G.N., "Hellenism in Ancient
Munshiram Manoharlal, New Delhi, 1961.
Manabandu, "Sanskrit
Journal of
Vastu Works
History of
India,
on Soil
Science
Banerjee
testing",
Vol.3l(3),
New Delhi.
Indian
1996, Indian National Science Academy,
8 Bhanumurthy. T.S., "A Modern Introduction to Ancient
Indian Mathematics", Wiley Eastern Limited, New
Delhi-2, 1992.
274
9 Bharati Kp~na Tirthaji, "Vedic Mathematics", Motila1
Banarsidas, Delhi-7, 1988.
10 BhOja, "Samar§nkaQa SGtradh~ra", Edited by
11
T. Ganapathi 'Sastri, M.S. University of Baroda, 1966.
Boner Alice, Sarma. S.R., Baurau.
Upani~ad", of Pippalada, (tr and
Banarsidas, Delhi.
B., "Vastusutra
summary), Motilal
12 Boyer. C.B., "The History of Mathematics", wiley,
New York, 1968.
13 Chandrasekhara Pillai. V. and Balakrishnanasari. S.
(Ed) "Vastuvidya", (Mal), Kerala Univeristy Oriental
14
15
16
Research Institute and Manuscript Library,
Trivandrum, 1979.
Chandrika. B.T., "Dravidasilpakala", (Mal),
Bhasha Institute, Trivandrum, April 1974.
Kerala
Cheriya Anujan Bhattathirippad. K. P. ,
Narayanan
Panchangam
"Tantrasamuchayam" (Mal) of Chennas
Namboothirippad, Parts I, 11 & Ill,
Pustakasala, Kunnamkulam, 1989.
Damodaran Namboothirippad. K., "Tant rasamuchayam"
(~ilpabhagam) (Mal), Panchangam Pustakasa1a,
Kunnamkulam, 1988.
17
275
Datta. B. & A.N.
Mathematics", A Source
Publishing House, Bombay,
Singh,
Book,
1962.
"History
Part I &
of
11,
Hindu
Asia
18 Dietz Albert. G.H., "Dwelling House Construction",
The MIT Press, Cambridge, 1979.
19 Fergussan Jarnes, "History of India and Eastern
Architecture", Vol.I, Edinburg Press, London, 1910.
20
21
Ganapathi Sastri.
(SKT), Trivandrum,
T. (Ed)
Sanskrit
Press, Trivandrum, 1919.
"Mayamata of
Ser ies No. LXV,
Mayamun i",
Government
Ganapathi Sastri. T.
(SKT), Trivandrum,
Trivandrum, 1922.
(Ed), "Silparatna of Srikumara",
Sanskrit Series No.LXXV,
22 Ganitanand, "A few remarks concerning certain values
of ~ in Ancient India", Ganita Bharati, Vol.12,
Nos.1-2, (1990).
23 Ghurye. G.S.,
Bombay, 1979.
"Vedic India", Popular Prakashan,
24 Gupta. R. C. , "On the value of ~ from the Bible",
GaQita Bharati, Vol.lO, Nos. 1-4 (1988).
276
25 Gupta. R.C., "South Indian Achievements in Medieval
Mathematics", Ganita BharatL Vo1.9, Nos. 1-4 (1987).
26 Gupta. R. C. , "Lindemanns discovery of the
Transcendence of ~. A century tribute, Ganita
Bharati, Vol.4, Nos. 3-4 (1982).
27 Heath. T. L. , "A History of Greek Mathematics",
Vol.II, Dover, New York.
28 Heath. T.L., "The Thirteen Books of the elements",
Second Edition, Vol.III, Books X-XIII and Appendix,
Dover, New York.
29 Jatavedan Namboothiri,
(Mal), Mathrubhumi Weekly,
1982.
"Kattil
Book
Mutal Kavilvare"
59, Vol.44, Page 6,
30 Kapila Vatsyayan, "The Art of Kerala Khetram", Edited
by Prof. K.G. Paulose, S.R.V. Govt. Sanskrit College
Committee, Trippunithura, 1989.
31 Kapur. J.N., "Review on Geometry in Ancient and
Medieval India", by T.A. Saraswati Amma, Indian
Journal o£ History of Sciences, Vol.24(1), 1989.
32 Kay. K.R., "The Bakhshali Manuscript", A study in
Medieval Mathematics, Part I & 11, Cosmo
Publications, New Delhi, 1981.
33
277
Kayalad. K.P., "Vastuvidyayute
Desabhimani Weekly, Book Nos.
to 34, 1996 & 1997.
Aksharamal a" (Mal) ,
28 and 29, Vols. 29
34 Kesavachari. N., Payyannur, Balaramam (Silpasastram),
(Mal), Vidyarambam Publications, Alappuzha, 1989.
35 Kesavachar i . N. , Payyannu r, "Gan i taratnakaram" ,
(Mal), Vidyarambam Publications, Alappuzha, 1989.
36 Kesavachar i. N. Payyannur, "Manushyal ayasopanam"
(Mal), Acharyagranthalayam, Payyannur, 1956.
37 Koy i that ta. N., "Manushyalayachandr i ka", (Mal), Al i ed
Publications, Talasseri, 1989.
38 Krarnrisch Stella, "The Hindu Temple", Vol.I & 11,
Motilal Banarsidass, Delhi, 1976.
39 Krishnan. T. V . (Tr) 11 Logan te Malabar Manuel" (Mal)
of Williarn Logan, Mathrubhumi, Calicut, 1985.
40
41
Krishnanasari
Vastuvidyabhyasarn"
Guruvayur, 1992.
Vazhappilli,
(Mal), Santha
"Silpakala
Book Stall,
Krishnanasari Vazhappilli, "Thachusastram" (Mal),
Santha Bookstall, Guruvayoor, 1992.
278
42 Krishnan Namboothiri Kanuppayyuri and Dr. A. Achyuthan
(Ed), "Readings in Vastusastra (Traditional
Architecture)",
1995.
Vastuvidyapratistanam, Kozhikode,
43 Krishna Warrier, Parakkal, "Grahanirmanapadhati"
(Mal), Panchangam Bookstall, Kunnamkulam, 1990.
44 Lockwood Michael, Gift Siromoney, P. Dayanandan i
"Mahabalipuram Studies", C.L.S., Madras, 1974.
45 Madhavaj i, "Kshetrachai tanyarahasyam", (Mal), Kerala
Kshetrasamrakshana Samiti, Kozhikode, 1988.
46 Madhavan.
Numerals" ,
Sanskrit
1991.
S. , "Origin of
S.R.V. Samskrita
College Committee,
Katapayadi
grantavali
Tripunithura,
System of
(J 1) , Gov t •
Vol. XVII,
47 Maheswaran Bhattathirippad, Kuzhikkat, "Kuzhikkat
Paccha" (Tantragrantham) (Mal), Panchangam Bookstall,
Kunnamkulam, 1991.
48 Mall ayya. N. V ., "Stud ies on Sanskr i t Texts on Templ e
Architecture with special reference to the
Tantrasamuccaya" , The Journal of the Annamalai
University, Vol.X, No.l & 2.
279
49 March. L. & Philip Steadman, "The Geometry of
Environment", MIT Press, Cambridge, 1974.
50 Moosad. C.K., "Prachinaganitam Ma1ayalathil" (Mal),
Kerala Bhasha Institute, Trivandrum, 1980.
51
52
53
54
Narayanan Kattumatam,
Mathrubhumi Weekly,
February 1992.
"Naveekaranakalasam"
Book 69, Vo1.51, Page
(Mal) ,
33,
Narayana Pisharoti. K.P., "Malaya1athile
Samkhyasabdangal" (Mal) , Mathrubhumi
69, Vol.2, Page 18, March 1991.
Weekly, Book
Nath. R. , "Agra and its Monumental Glory",
Taraporevala Sons & Co. (P) Ltd., 1977.
Neelakandanasari.
(with commentary)
1987.
K., "Manushyalayamahachandrika"
(Mal), S.T. Redyar & Sons, Ko11am,
55 Neelakandanasar i. K., 11 Manu shyal ayav idh i " (Mal), Dev i
Bookstall, Kodungallur, 1981.
56 Parameswaran. K. (Ed) , "Manushya1ayachandrika"
(Thachusastram) (Mal), Kochi Malaya1abhasha
Pariskarana Committee, 2nd edition, (1125 ME).
57
280
Prabhu Balagopal. T.S., "Vastuvidyadarsanam"
Vastuvidyapratistanam, Kozhikode, 1994.
(Mal) ,
58 Prabhu Balagopal. T.S.; & Dr. A. Achyuthan, "A Text
Book of Vastuvidya", Vastuvidyapratistanam, Calicut.
59
60
Prabhu Balagopal. T. S. , (Ed) , "Vastuvidya 95",
Selected Papers of National Conference on Vastuvidya,
Calicut, 1995.
Prabhu Balagopal. T.S. & Dr. A.
"Keralathinte Thachusastram", Mathrubhumi
Book 63, Vol.8, Page 26, May 1985.
Achyuthan,
Weekly,
61 Pramar. V.S., "Design Fundamentals in Architecture",
Somaiya Publications, Bombay.
62 Purushothaman
Varahisamhita"
Press, Kollam,
Namboothiri. P.S., "Brhalsamhita or
(commentary), (Mal), Sriramavilasam
1935.
63 Purushothama Sarma. C.S., "Yantrasamuccayam", (Mal),
Devi Bookstall, Kodungallur, 1997.
64 Raghava Varrier.
(Mal), Mathrubhumi
March 1988.
M.R., "Kodungalloorinte Patanam",
Weekly, Book 65, Vol.52, Page 26,
65
281
Ramachandra Men on. P. , "Bharateeyagan i tarn"
Kerala Bhasha Institute, Trivandrum, 1989.
(Ma 1 ) ,
66 Ramavarma (Maru) Thamburan & A. R. Akh ileswara Iyer,
67
68
69
"Yuktibhasha" (Mal) , Mangalodayam Ltd. , Trichur,
1948.
Ramesh. R.K., "Veeduka10
Mathrubhurni Weekly, Book
1990.
Kongreetukootukalo?" (Mal),
68, Vol.ll, Page 30, May
Rao Balachandran. 5., "Indian Mathematics
Ast ronorny" , Jnanadeep Publ icat ions, Bangalore
1994.
and
10,
Rao Muralidhar, "Vaastu Shilpa Saastra", S.B.S.
Publications, Bangalore, January 1995.
70 Sankaran Namboothirippad, Kanippayyur,
. "Manushyalayachandr ika" , (Mal), Pan changam Bookstall,
Kunnarnkularn, (1162 ME).
71 Sankaran Namboothirippad, Kanippayyur, "Kaikanakkum
Atamkal Pattikayurn", (Mal), Panchangam Bookstall,
Kunnarnkularn, (1166 ME).
72 Sankaran Narnboothirippad, Kanippayyurr
UMuhurthapadav i" , (Mal) , Panchangam Booksta 11,
Kunnarnkularn, (1168 ME).
282
73 Sarada Srinivasan, "Mensuration in Ancient India",
Ajanta Publications, Delhi, 1979.
74 Sarbhai. S.C., "Review on
Contributions to Mathematics"
Vo1.12, No.1-2, (1990).
Aryabhata I
by Parameswar
and
Sha,
his
GB,
75 Sarma. K. V., "A History of the Kerala School of Hindu
Astronomy" ,
1972.
Vishveshvaranand Institute, Hoshiarpur,
76 'Sarma. K.V., (Ed), "Tantrasangraha of Nilakantha
77
Somayaji with Yuktidipika and Laghuvivrti of
Sankara", V.V.B.I. of Sanskrit and Ido1ogica1
Studies, Punjab University, Hoshiarpur, 1977.
Sarmak. V. and
Jyestadeva", Indian
Vo1.26, No.2, 1991.
S. Hariharan, "Yuktibhasa of
Journal of History of Sciences,
78 'Sarma. K. V • I 11 Leelava ti of Bhaskaracarya", (SKT),
V.V.R.I. Hoshiarpur, 1975.
79
80
'Sarma. V. S. ,
Bhaktapriya, Book
1986.
"Vastu Sutra Upanishad", (Mal),
I, Vol.6, Page 54, Guruvayur, June
Sasibhushan.
Mathrubhumi
1982.
M. G. ,
Weekly,
"Chuvaruka1: Chitranga1",
Book 59, Va1i 44, PP 5,
(Mal) ,
January
81
82
83
283
Sasirupan, "Chatussalakalku
(Mal), Mathrubhumi Weekly,
July 1990.
oru charamakkurippu" ,
Book 68, Vol.21, pp 8,
Shukla. A.K., "Mathematics of Aesthetics",
Publisher Pvt. Ltd., New Delhi - 21, 1987.
Enkey
Soundara Rajan. K.V., "Indian Temple
Munshiram Manoharlal, New Delhi, 1972.
Styles" ,
84 Srinivasan. K.R., "Temples of South India", National
Book Trust India, New Delhi, 1972.
85 Srinivasan. P.R., "Beginnings of the Tradition of
South Indian Temple Architecture", a Bulletin of the
Madras Govt. Museum, New Series, Vol.VII, No.4, 1959.
86 Vamanan. K. K. , "Sreechakram" , (Mal) , Mathrubhum i
Weekly, Book 67, Vol.32, pp 43, October 1989.
87 Varahamihira, "Brhat Samhita", (Tr) by V. Subrahmanya
Sastri and Ramakrishna Bhat, Published by V. B.
Soobbiah & Sons, Bangalore, 1947.
88 Vasuachari, Tannirmukkam, "Silpibalaprabodhini",
(Mal), Vidyarambam Publishers, Alappuzha, 1992.
89 Vasuachari,
Sastram)" ,
1990.
Tannirmukkam,
(Mal), Vidyarambam
"Grhachitravali (Silpa
Publishers, Alappuzha,
284
90 Vasuachar i, Tannirmukkam, "Vastukaumudi" , (Mal) ,
Vidyarambam Publishers, Alappuzha, 1992 0
91 Vasudeva Sastri & NoB. Gadre, (Ed), "Viswakarma Vas tu
92
Sastram"
Tanjore,
Waerden 0
(text
1958.
BoLo,
Civilizations",
and commentary), T.M.SoS.M. Library,
"Geometry and Algebra
Springer - Verlag, Berlin,
in Ancient
19830
GLOSSARY
Adhisth~na: Basement .. structure, forming
support ing walls
of a vimana, maryQapa, or similar
a distinct architectural feature,
and pillars, and consisting of
distinct moulded tiers.
~dharasila: Foundation stone generally used to denote
the idol. the lowest part of the support system of
Ali~da: Corridor, varanta, passage.
Alpapras~da: Small temple with the
Prasada (Srikov i 1) not ex ceeding
single storey.
perimeter
16 hasta
of the
and of
Angula: Linear measurement equal to 1/64 of vyama; also
equal to 8 yava. 1 angula is 3 cm.
AnkaQa: Courtyard
AnkaQasGtras:
courtyard.
Axes passing through the centre of the
Antah~ra: Secondary boundary of temple from prasada.
~ntara bhitti:
or sanctum.
Antarmandala:
usually at
prasada.
Inner wall of multiple walled prasada
The innermost prakara around the sanctum
a distance of half the width of the
286
Ara: Room; chamber, the traditional architectural
construction of Kerala in which the walls of the rooms
are constructed in wood is called 'ara' and Inira'.
Ardha-maQ9apa: Pillared hall immediately in front of
the pr inc ipal shrine or d i stal hal f of a mandapa wi th
two seriate pillars, as in rockcut cave-temple.
Arddhadhika: Ratios of length to width which are
obtained by adding ~ to integers.
Arodh6thara (Arudham) : , Additional horizontal support
for the ra fters between wallpla te and ridge; el eva ted
uttara.
Asiddha: Temple sites in settlements.
Astavarga: 8 x 8 grid; ma~?uka ma~9ala.
Ayama: Elongation; the frontal elongation is called
mukhayama.
Ayatacaturasra: Rectangle.
Bahya-bhitti:
sanctum.
Outermost wall of a multiple-walled
Bahya-h§ra:
prasada.
Fourth boundary of the temple from the
Balivattam:
(balikkal).
287
Envelope containing the offering stones
Bhadra:
with
Land
good
located at the side of sea, river or lake
resource of water and facilities for
cultivation.
Brahmanabh i: Focal point of a vastumat;l9a1a, where the
two sutras intersect.
BrahmasGtra: The west-east axis of a maD?ala.
Chitra-potika: Corbels with embossed carving or painting
of creepers, flowers etc.
Cuttampalam: The covered corridor
room located 1 dandu away from
called nalampalam.
encl os ing the shr ine
the shr ine-room ~ also
Da1)9u: Linear measurement equal to 4 hasta (96 angula),
the unit in the proportional system of measurement.
DhGmra: This is an inferior variety of arid site.
Eaves: The lowest part of the roof. It is the section
formed by the rafter ends, plate, and cornice.
Gable: The gable roof consists of two inclined planes
which meet in a
and slope down
peak over the centre line of the house
to two oppos i te roof plates. At the
288
two ends are triangular sections of wall called
"gables" or "gable-ends", hence the name gable roof.
Gaj apr~~ha: Combination of square and semi -c i reI e: the
rear side of an elephant.
Garbhagfha: Shrine-cell or cellar.
Grhavastu: Architecture of residential buildings.
Gala, griva: Neck, usually the clerestory raising up
the roof wi th light and ai r open ings (Nas ikas) on its
sides.
Hasta: ~nthropometric linear measurement equal to length
of arm~ the standard and most commonly used hasta is
24 angula and is called ki~ku; 8 types of hastas
varying from 24 angula to 31 angula with variation
of 1 angula are known by different names; the names
for hasta are kara, bhuja, aratni, kol.
Hip: When the roof slopes down in four inclined planes
to four plates, it is called a hip roof.
11:IanakhaJ')c;'ia: The sector of Isa I the north-east sector;
also called manu~yakha~c;'ia.
tstadirgha: Desired length, selected length . . .
289
Kadalakakarna : Successive inward off set t ing or
corbelling of the roofing slabs or brick courses over
walls to reduce the space to be roofed over to an
ultimate small opening top that can be covered by a
slab overlapping like a banana bunch.
Kala~a: The pot of the lower portion of the finial.
Kar~asGtra: Diagonal axis of a map9ala.
Katapayadi notation: A system
system the
of representation of
consonants (vyanjanas) numbers. In this
beginning with ka, ta, pa and ya represent the digits
from 1. Pa to ma stand for 1 to 5 and ya to ha
represent digits 1 to 8. m and n denote O. In the
case of conj unct consonants, the number denoted only
by the last consonant is taken and the vowels
following
preceded
represents
digits is
consonants have no value. The vowels not
by consonants represent O. The letter 1
9. In th is system the arrangement of the
from right to left (ankanam vamato gati).
Kavu: Sacred grove, f or the worship of gods 1 ike Kal i ,
Ayyappan, Serpents etc.
KhanQottara: Uttara having equal width and thickness
is called khaQQottara.
Kila: Wedge.
290
K~etravastu: Architecture of temple.
Kuta :
the
Pendant: solid wooden piece to which tip of all
rafters of a ko~ta type of roof or the top ends
of slanting rafters and the end of ridge of a sabha
type of roof are connected.
Kuthampalam: Temple theatre tor performing arts.
Madhyama: Medium.
Madhyahara:
dlpam§la.
Mahamarma:
a mal}?ala.
Third boundary of a temple comprising the
Sensitive node when 4 sutras intersect in
Mandala: . . Demarcated area: region, generally circular.
Marygapa: Open or closed pillared or astylar hall.
Manu~yalaya: House for human beings.
Manu~yapramarya: Measurement system based on the size
and proportions of human body.
Marmav~dha: Intersections with vulnerable points.
Maryada: Fifth boundary of a temple: outermost pr~kara.
291
Matra: Module of measurement.
Mi'sra: Mixed.
Namaskaramaryqapa:
for namaskara.
Pav il ion in fron t of the prasada used
Natyasala: Halls for performing arts.
Navavarga: 9 x 9 grid, parama~ayikamaryqala.
N~pathya: Makeup room, aryiyara.
Oma: Basal pitha of pillar or pilaster.
Pada: Linear measurement equal to 8 angula; pillar.
Padma: Lotus, capital-member below the phalaka.
Parivara devatas: Subsidiary deities in a temple.
Patrottara: Uttara having thickness 3/4 of the width
is called Patrottara.
Patta: Plain or decorated band.
Pattika: Projected top slab of the platform or
adhi~t~na, or wooden reaper.
292
Ratios of length to width which are obtained
by adding ~ to integers.
Plldona: Ratios of length to width which are obtained
by subtracting ~ from integers greater than 1.
P~duka: Ground course, the lowest part of the adhi~tana.
Phalaka: Abacus, moulded capital of pillar supporting
the corbel, or potika.
Pinjara: Wooden roof-frame.
Poorna: These types of sites are located on top of
plateaus or in the mountain valleys.
Potika: Corbel bracket over pillar.
Pra~~!a: spout projected to discharge water.
Prasada: Sreekovil or vimana.
Prastara: En tablature, con sist ing of mould ing s over
walls and pillars, viz, the uttara (beam).
Pitch: The 'pitch' of a roof is its slope.
Piija: Adoration; sacrifice to the deity, offerings and
other rites.
293
Rafters: These are the structural members of the roof.
Common rafters or straight rafters run from ridge to
plate at right angles to the wall. The hip rafters
run from the exterior corners of the plate to the ends
of the ridge. Framing into the hips are shorter
rafters, runn ing from· pIa te to hip raf ter, call ed jack
rafters.
Raj ju: Linear measurement equal to 8 dandu I 1 i terally
means rope; also, the diagonal sGtra in a mandala.
Ridge: The peak of the roof. The ridge board or ridge
pole is the member against which the rafters bear.
It forms the lateral tie which holds them together
at that point. In a square house the ridge vanishes
to a point or kootam.
ROpottara: Uttara having thickness ~ of the width is
called Rupottara.
S::Ua: Rectangular hall wi th gable roof, in some cases
it represent a courtyard house.
Samatatam: A rectangle with length equal to an integer
multiple of its width.
Sikhara: Roof of the pdisada, domical, 4 sided wi th a . single fin ia1, vaul ted wi th many finial s on the ridge I
or apsidal with many finials.
294
Slista- Bhinnasala: Catussala with partially separated . and partially combined halls (houses).
S~pana: Flight of steps.
Srlkov il: Used to denote v imana or prasada, the sacred
structure.
Sthapati:
person
One
in
of
all
the four
types of
'samaitakriyipatu' .
stupika: ( Stupi) Fin ial .
silpins who is the relevent
construction, must be a
Supadma: It is a land located in the plains, suitable
for human habitation and temples.
Sutragrahi: He must be wellversed in all sastras,
constructions etc. a student of Sthapati or his son.
Another silpin of the 4 silpins.
Tak?aka: The third silpin in the construction of houses.
Tala: Storey of the temple, gopura.
Tala: A proport ionate measure, palm of the hand, modul ar
unit of dimension in iconography in terms of face
length.
295
Taranga: Wave.
Upapi~ha: Add i tional mou Ided platform or sub-base below
the adhistana. . .
Vardhaki: The fourth silpin in the construction of
bu i lding .
Vilakkumadam: The structure with several rows of oil
lamps at the Madhyahara.
Vimana: Prasada, Srikovil.
Vyala: Leonine figure.
Yoni: Architectural formula for orientation, place of
origin.
**********