95055934 Add Math Project Work 2012

7/28/2019 95055934 Add Math Project Work 2012

1/44

SEKOLAH BERASRAMA PENUH INTEGRASI GOMBAK

ADDITIONALMATHEMATICS PROJECT

WORK 2012

NAME : MAISARAH BINTI ZAINUDDIN

CLASS : 5 IBNU NAFIS

I/C NO : 950201-14-5724


2/44

ADDITIONAL MATHEMATICS PROJECT WORK 2012

2 SEKOLAH BERASRAMA PENUH INTEGRASI GOMBAK | POLYGON

INDEX


3/44



INDEX

NO CONTENT PAGE

1. INDEX 2-32. ACKNOWLEDGEMENT 4-53. OBJECTIVES 6-84. INTRODUCTION 9-145. PART 1 15-216. PART 2 22-257. PART 3 26-368. FUTHER EXPLORATION 37-409. CONCLUSION 41-42

10.

REFLECTION 43-44


4/44



ACKNOWLEDGEMENT


5/44



ACKNOWLEDGEMENT

After a week of struggle and hard work to complete assignment given to us by our

teacher, Puan Che Gayah, I finally did it within a week with satisfaction and senses of success

because I have understood more deeply about the interest and investment more than before. I am

very grateful and thankful to all parties who has helped me in the process of completing my

assignment. It was a great experience for me as I have learnt to be more independent. For this, I

would like to take this opportunity to express my thankfulness once again to all parties

concerned.

Firstly, I would like to thank my Additional Mathematics teacher, Puan Che Gayah for

patiently explained to us the proper and precise way to complete this assignment. With her help

and guidance, many problems I have encountered had been solved.

Besides that, I would like to thank my parents for all their support and encouragement

that have been given to me. In addition, my parents had given me guidance in the methods to

account for investment which have greatly enhanced my knowledge on particular area. Last but

not least, I would like to express my thankfulness to my fellow friends, who have patiently

explained to me and together with me completing this project.


6/44



OBJECTIVES


7/44



OBJECTIVES

Every student taking Additional Mathematics is required to carry out a project work

while they are in form 5. For this year, the Curriculum Development Division, Ministry of

Education has prepared several tasks. Students are to choose and complete only ONE task based

on their area of interest. Upon completion of the project, it is hoped that students will gain

valuable experiences and able to:

a) Apply and adapt a variety if problem-solving strategies to solve routine and non-routine

problems.

b) Experience classroom environment which are challenging, interesting and meaningful and

hence improve their thinking skills.

c) Experience classroom environment where knowledge and skills are applied in meaningful

ways in solving real-life problems.

d) Experience classroom environment where expressing ones mathematical thinking,

reasoning and communication are highly encouraged and expected.

e) Experience classroom environment that stimulates and enhances effective learning.

f) Acquire effective mathematical communication through oral and writing, and to use the

language of mathematics to express mathematical ideas correctly and precisely.

g) Enhance acquisition of mathematical knowledge and skills through problem-solving ways

that increase interest and confidence.


8/44



h) Prepare students for demands of their future undertakings and in workplace.

i) Realise that mathematics is an important and powerful tool in solving real-life problems and

hence develop positive attitude towards mathematics.

j) Train them not only to be independent learners but also to collaborate, to cooperate and to

share knowledge in an engaging and healthy environment.

k) Use technology especially the ICT appropriately and effectively.

l) Train them to appreciate the intrinsic values of mathematics and to become more creative

and innovative.

m) Realise the importance and the beauty of mathematics.


9/44



INTRODUCTION


10/44



INTRODUCTION

In geometry a polygon is a flat shape consisting of straight lines that are joined to form a

closed chain or circuit.

A polygon is traditionally a plane figure that is bounded by a closed path, composed of a

finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are

called its edges or sides, and the points where two edges meet are the polygon's vertices

(singular: vertex) or corners. An n-gon is a polygon with n sides. The interior of the polygon is

sometimes called its body. A polygon is a 2-dimensional example of the more general polytope

in any number of dimensions.

The word "polygon" derives from the Greek (pols) "much", "many" and

(gna) "corner" or "angle". (The word gnu, with a short o, is unrelated and means

"knee".) Today a polygon is more usually understood in terms of sides.

The basic geometrical notion has been adapted in various ways to suit particular

purposes. Mathematicians are often concerned only with the closed polygonal chain and with

simple polygons which do not self-intersect, and may define a polygon accordingly.

Geometrically two edges meeting at a corner are required to form an angle that is not straight

(180); otherwise, the line segments will be considered parts of a single edgehowever

mathematically, such corners may sometimes be allowed. In fields relating to computation, the

term polygon has taken on a slightly altered meaning derived from the way the shape is stored

and manipulated in computer graphics (image generation).


11/44



HISTORY

Polygons have been known since ancient times. The regular polygons were known to the

ancient Greeks, and the pentagram, a non-convex regular polygon (star polygon), appears on the

vase of Aristophonus, Caere, dated to the 7th century B.C.[citation needed] Non-convex

polygons in general were not systematically studied until the 14th century by Thomas

Bradwardine.

In 1952, Geoffrey Colin Shephard generalized the idea of polygons to the complex plane,

where each real dimension is accompanied by an imaginary one, to create complex polygons.

Historical Image of Polygon


12/44



ANGLES OF POLYGON

Any polygon, regular or irregular, self-intersecting or simple, has as many corners as it

has sides. Each corner has several angles. The two most important ones are:

Interior angle The sum of the interior angles of a simple n-gon is (n2) radians or(n2)180 degrees. This is because any simple n-gon can be considered to be made up of (n 2)

triangles, each of which has an angle sum of radians or 180 degrees. The measure of any

interior angle of a convex regular n-gon is radians or degrees. The interior angles of regular star

polygons were first studied by Poinsot, in the same paper in which he describes the four regular

star polyhedra.

Exterior angle Tracing around a convex n-gon, the angle "turned" at a corner is theexterior or external angle. Tracing all the way around the polygon makes one full turn, so the

sum of the exterior angles must be 360. This argument can be generalized to concave simple

polygons, if external angles that turn in the opposite direction are subtracted from the total

turned. Tracing around an n-gon in general, the sum of the exterior angles (the total amount one

rotates at the vertices) can be any integer multiple d of 360, e.g. 720 for a pentagram and 0

for an angular "eight", where d is the density or starriness of the polygon.

The exterior angle is the supplementary angle to the interior angle. From this the sum of

the interior angles can be easily confirmed, even if some interior angles are more than 180:

going clockwise around, it means that one sometime turns left instead of right, which is counted

as turning a negative amount. (Thus we consider something like the winding number of the

orientation of the sides, where at every vertex the contribution is between 12 and 12 winding.)


13/44



POLYGONS IN NATURE

Numerous regular polygons may be seen in nature. In the world of geology, crystals have

flat faces, or facets, which are polygons. Quasicrystals can even have regular pentagons as faces.

Another fascinating example of regular polygons occurs when the cooling of lava forms areas of

tightly packed hexagonal columns of basalt, which may be seen at the Giant's Causeway in

Ireland, or at the Devil's Postpile in California.

The most famous hexagons in nature are found in the animal kingdom. The wax

honeycomb made by bees is an array of hexagons used to store honey and pollen, and as a secure

place for the larvae to grow. There also exist animals who themselves take the approximate form

of regular polygons, or at least have the same symmetry. For example, sea stars display the

symmetry of a pentagon or, less frequently, the heptagon or other polygons. Other echinoderms,

such as sea urchins, sometimes display similar symmetries. Though echinoderms do not exhibit

exact radial symmetry, jellyfish and comb jellies do, usually fourfold or eightfold.

Radial symmetry (and other symmetry) is also widely observed in the plant kingdom,

particularly amongst flowers, and (to a lesser extent) seeds and fruit, the most common form of

such symmetry being pentagonal. A particularly striking example is the star fruit, a slightly tangy

fruit popular in Southeast Asia, whose cross-section is shaped like a pentagonal star.

Moving off the earth into space, early mathematicians doing calculations using Newton's

law of gravitation discovered that if two bodies (such as the sun and the earth) are orbiting one

another, there exist certain points in space, called Lagrangian points, where a smaller body (such

as an asteroid or a space station) will remain in a stable orbit. The sun-earth system has five

Lagrangian points. The two most stable are exactly 60 degrees ahead and behind the earth in its


14/44



orbit; that is, joining the center of the sun and the earth and one of these stable Lagrangian points

forms an equilateral triangle. Astronomers have already found asteroids at these points. It is still

debated whether it is practical to keep a space station at the Lagrangian pointalthough it would

never need course corrections, it would have to frequently dodge the asteroids that are already

present there. There are already satellites and space observatories at the less stable Lagrangian

points.

Star fruit, a popular fruit in Southeast Asia

The Giant's Causeway, in Northern Ireland


15/44



PART 1


16/44



QUESTION (a) - Pictures of Polygons

The Egyptian Pyramids are ancient pyramid-shape masonry structures located in Egypt.

Contemporary Home Design in polygon-shaped with marvelous panorama at the Pittman Dowell

Residence


17/44



The Kaaba is a cuboid-shaped building in Saudi Arabia, Macca.

Rectangular-shaped bricks.


18/44



Pentagon-shaped tiles.

Trapezium-shaped house.


19/44



QUESTION (b) Definition and History of Polygons

Polygon is a closed shape consisting of line segments that has at least three sides.

Triangles, quadrilaterals, rectangles, and squares are all types of polygons.

The word "polygon" comes from Late Latin polygnum (a noun), from Greek

(polygnon/polugnon), noun use of neuter of (polygnos/polugnos, the masculine

adjective), meaning "many-angled". Individual polygons are named (and sometimes classified)

according to the number of sides, combining a Greek-derived numerical prefix with the suffix -

gon, e.g. pentagon, dodecagon. The triangle, quadrilateral or quadrangle, and nonagon are

exceptions. For large numbers, mathematicians usually write the numeral itself, e.g. 17-gon. A

variable can even be used, usually n-gon. This is useful if the number of sides is used in a

formula. Some special polygons also have their own names; for example the regular star

pentagon is also known as the pentagram.

Polygons have been known since ancient times. The regular polygons were known to the

ancient Greeks, and the pentagram, a non-convex regular polygon (star polygon), appears on the

vase of Aristophonus, Caere, dated to the 7th century B.C. Non-convex polygons in general were

not systematically studied until the 14th century by Thomas Bredwardine. In 1952, Shephard

generalized the idea of polygons to the complex plane, where each real dimension is

accompanied by an imaginary one, to create complex polygons.


20/44



QUESTION (c) Methods of Finding Area of Triangle

1.

2.


21/44



3.

4. | |


22/44



PART 2


23/44



QUESTION (a) Cost Needed

Cost = RM 20 300 = RM 6000

QUESTION (b) Completing The Table Given

p(m) q(m) (degree) Area(m)60 140 38.21 2597.89

70 130 49.58 3463.97

80 120 55.77 3968.57

90 110 58.99 4242.53

100 100 60.00 4330.13

110 90 58.99 4242.53

120 80 55.77 3968.57

130 70 49.58 3463.97

140 60 38.21 2597.89


24/44



Question (c) Dimension of The Herb Garden

The herb garden is an equilateral triangle of sides 100m with a maximum area of

4330.13m.

CONJECTURE

Regular polygon will give maximum area.

Eg:

Square

Rectangle


25/44



QUESTION (d) Values ofpand q

i. 60


26/44



PART 3


27/44



QUESTION (a) Five Suggestions

i. Quadrilateral2 + 2 = 300 m

+ = 150 mArea =

The maximum area is 5625 m.

ii. Regular Pentagon

tan

Area = 10 140 1400

20 130 2600

30 120 360040 110 4400

50 100 5000

60 90 5400

70 80 5600

75 75 5625

m

m


28/44



iii. Regular Hexagon

tan

iv. Regular Octagon

tan 67.5 tan

v. Regular Decagon

tan tan


29/44



QUESTION (b) (i) Herbs

1.Misai Kucing (Orthosiphon stamineus)Orthosiphon is a medicinal plant native to South East Asia

and some parts of tropical Australia. It is an herbaceous shrub which

grows to a height of 1.5 meters. Orthosiphon is a popular garden

plant because of its unique flower, which is white and bluish with

filaments resembling a cat's whiskers. In the wild, the plant can be

seen growing in the forests and along roadsides.

Common names in Southeast Asia are Misai Kucing

(Malaysia), Kumis Kucing and Remujung (Indonesia), and Yaa Nuat Maeo (Thailand). The

scientific names are Orthosiphon stamineus Benth, Ocimum aristatum BI and Orthosiphon

aristatus (Blume).

Medicinal Uses

Orthosiphon is used for treating the ailments of the kidney, since it has a mild diuretic effect. It is

also claimed to have anti-allergenic, anti-hypertensive and anti-inflammatory properties, and is

commonly used for kidney stones and nephritis. Orthosiphon is sometimes used to treat gout,

diabetes, hypertension and rheumatism. It is reportedly effective for anti-fungal and anti-

bacterial purposes.

How To Cure

In Malaysia, people eat the leaves raw. They take a few leaves, heat them with water to make the

water bitter, and then mix it with tea bags.
http://en.wikipedia.org/wiki/Nephritishttp://en.wikipedia.org/wiki/Gouthttp://en.wikipedia.org/wiki/Diabeteshttp://en.wikipedia.org/wiki/Hypertensionhttp://en.wikipedia.org/wiki/Rheumatismhttp://en.wikipedia.org/wiki/Rheumatismhttp://en.wikipedia.org/wiki/Hypertensionhttp://en.wikipedia.org/wiki/Diabeteshttp://en.wikipedia.org/wiki/Gouthttp://en.wikipedia.org/wiki/Nephritis


30/44



Research

Orthosiphon began to interest researchers early in the 20th century, when it was introduced to

Europe as a popular herbal health tea.

Commercial products

Orthosiphon is available in many products treating for detoxification, water retention,

hypertension, obesity or kidney stones. It comes in tablets, capsules, tea sachets, bottled drinks,

raw herbs, dried leaves or extracts.


31/44



2.Kacip Fatimah (Labisia Pumila)Kacip fatimah (Labisa pumila) is the female version ofTongkat Ali. Kacip Fatimah is a

small woody and leafy plant that grows and can be

found widely in the shade of forest floors. The leaves

are about 20 centimeters long, and they are

traditionally used as a kind of tea by women who

experience a loss of libido. Despite its long history of

traditional use, the active components and mode of

action have not been well studied, though some preliminary research has been published.

Uses

Extract from these herbs is usually ground into powder substances and are made into capsules

and pills. A concoction made from boiling the plant in water is given to women in labour to

hasten delivery of their babies. After childbirth, it may still be consumed by mothers to regain

their strength. In other medicinal preparations, it can treat gonorrhoea, dysentery and eliminate

excessive gas in the body.

Traditionally, it is used in Borneo for enhancing vitality, overcome tiredness and help to tone

vaginal muscles for women.

The claimed uses of Kacip Fatimah include:

Helps establish a regular menstrual cycle when periods fail to appear for reasons likestress, illness or when the pill is discontinued

Prevents cramping, water retention and irritability for those with painful periods.
http://en.wikipedia.org/wiki/Tongkat_Alihttp://en.wikipedia.org/wiki/Tongkat_Ali


32/44



Balances, builds and harmonizes the female reproductive system to encourage healthyconception

Supports healthy vaginal flora to prevent irritation and infections. Alleviates fatigue, smooths menopausal symptoms and promote emotional well being. Prolong energy during Playtime. Helps to solve the problems related to constipation Tightens vaginal skin and walls. Anti-dysmenorrhoea; cleansing and avoiding painful or difficult menstruation

Anti-flatulence, drive away and prevent the formation of gas.

Firming and toning of abdominal muscles.

As the plant containsphytoestrogen, it is not to be taken by pregnant women and periods of

menstruation.
http://en.wikipedia.org/wiki/Vaginal_florahttp://en.wikipedia.org/wiki/Dysmenorrhoeahttp://en.wikipedia.org/wiki/Phytoestrogenhttp://en.wikipedia.org/wiki/Phytoestrogenhttp://en.wikipedia.org/wiki/Phytoestrogenhttp://en.wikipedia.org/wiki/Phytoestrogenhttp://en.wikipedia.org/wiki/Dysmenorrhoeahttp://en.wikipedia.org/wiki/Vaginal_flora


33/44



3.Tongkat Ali (Eurycoma Longifolia)Eurycoma longifolia (commonly called tongkat ali or pasak

bumi) is a flowering plant in the family Simaroubaceae, native to

Indonesia, Malaysia, and, to a lesser extent, Thailand, Vietnam, and

Laos. It is also known under the names penawar pahit, penawar bias,

bedara merah, bedara putih, lempedu pahit, payong ali, tongkat

baginda, muntah bumi, petala bumi (all the above Malay); bidara laut

(Indonesian); babi kurus (Javanese); cay ba binh (Vietnamese) and tho

nan (Laotian). Many of the common names refer to the plant's medicinal use and extreme

bitterness. "Penawar pahit" translates simply as "bitter charm" or "bitter medicine". Older

literature, such as a 1953 article in the Journal of Ecology, may cite only "penawar pahit" as the

plant's common Malay name.

Growth

Eurycoma longifolia is a small, evergreen tree growing to 15 m (49 ft) tall with spirally

arranged, pinnate leaves 2040 cm (816 inches) long with 1341 leaflets. The flowers are

dioecious, with male and female flowers on different trees; they are produced in large panicles,

each flower with 56 very small petals. The fruit is green ripening dark red, 12 cm long and

0.51 cm broad.

Products

Fake Eurycoma longifolia products have been pulled off the shelves in several countries

but are still sold over the Internet, mostly shipped from the UK.

In a medical journal article, published March 2010, it was noted
http://en.wikipedia.org/wiki/Flowering_planthttp://en.wikipedia.org/wiki/Simaroubaceaehttp://en.wikipedia.org/wiki/Indonesiahttp://en.wikipedia.org/wiki/Malaysiahttp://en.wikipedia.org/wiki/Thailandhttp://en.wikipedia.org/wiki/Vietnamhttp://en.wikipedia.org/wiki/Laoshttp://en.wikipedia.org/wiki/Journal_of_Ecologyhttp://en.wikipedia.org/wiki/Evergreenhttp://en.wikipedia.org/wiki/Treehttp://en.wikipedia.org/wiki/Pinnatehttp://en.wikipedia.org/wiki/Leafhttp://en.wikipedia.org/wiki/Flowerhttp://en.wikipedia.org/wiki/Plant_sexualityhttp://en.wikipedia.org/wiki/Paniclehttp://en.wikipedia.org/wiki/Petalhttp://en.wikipedia.org/wiki/Fruithttp://en.wikipedia.org/wiki/Fruithttp://en.wikipedia.org/wiki/Petalhttp://en.wikipedia.org/wiki/Paniclehttp://en.wikipedia.org/wiki/Plant_sexualityhttp://en.wikipedia.org/wiki/Flowerhttp://en.wikipedia.org/wiki/Leafhttp://en.wikipedia.org/wiki/Pinnatehttp://en.wikipedia.org/wiki/Treehttp://en.wikipedia.org/wiki/Evergreenhttp://en.wikipedia.org/wiki/Journal_of_Ecologyhttp://en.wikipedia.org/wiki/Laoshttp://en.wikipedia.org/wiki/Vietnamhttp://en.wikipedia.org/wiki/Thailandhttp://en.wikipedia.org/wiki/Malaysiahttp://en.wikipedia.org/wiki/Indonesiahttp://en.wikipedia.org/wiki/Simaroubaceaehttp://en.wikipedia.org/wiki/Flowering_plant


34/44



that "estimates place the proportion of counterfeit medications sold over the Internet from 44%

to 90%" with remedies for sexual dysfunction accounting for the greatest share. It is therefore

recommended that buyers of Eurycoma longifolia request from Internet vendors conclusive

information, and proof, on the facilities where a product has been manufactured.

In Malaysia, the common use of Eurycoma longifolia as a food and drink additive,

coupled with a wide distribution of products using cheaper synthetic drugs in lieu of Eurycoma

longifolia quassinoids, has led to the invention of an electronic tongue to determine the presence

and concentration of genuine Eurycoma longifolia in products claiming to contain it.

On the other hand, consumers who lack the sophisticated electronic tongue equipment

invented in Malaysia for testing the presence of Eurycoma longifolia, but want more clarity on

whether the product they obtained is indeed Eurycoma longifolia or a fake, can use their own

tongue to taste the content of capsules for the bitterness of the material. Quassinoids, the

biologically active components of Eurycoma longifolia root, are extremely bitter. They are

named afterquassin, the long-isolated bitter principle of the quassia tree. Quassin is regarded the

bitterest substance in nature, 50 times more bitter than quinine. Anything that isn't bitter, and

strongly so, cannot contain quassinoids from Eurycoma longifolia .

In the US, the FDA has banned numerous products such as Libidus, claiming to use

Eurycoma longifolia as principal ingredient, but which instead are concoctions designed around

illegal prescription drugs, or even worse, analogues of prescription drugs that have not even been

tested for safety in humans, such as acetildenafil. In February 2009, the FDA warned against

almost 30 illegal sexual enhancement supplements, but the names of these products change

quicker than the FDA can investigate them. Libidus, for example, is now sold as Maxidus, still
http://en.wikipedia.org/w/index.php?title=Quassinoids&action=edit&redlink=1http://en.wikipedia.org/wiki/Quassinhttp://en.wikipedia.org/wiki/Quassiahttp://en.wikipedia.org/wiki/Quininehttp://en.wikipedia.org/wiki/Acetildenafilhttp://en.wikipedia.org/wiki/Acetildenafilhttp://en.wikipedia.org/wiki/Quininehttp://en.wikipedia.org/wiki/Quassiahttp://en.wikipedia.org/wiki/Quassinhttp://en.wikipedia.org/w/index.php?title=Quassinoids&action=edit&redlink=1


35/44



claiming Eurycoma longifolia (tongkat ali) as principal ingredient. The government of Malaysia

has banned numerous fake products which use drugs like sildenafil citrate instead of tongkat ali

in their capsules. To avoid being hurt by bad publicity on one product name, those who sell fake

tongkat ali from Malaysia have resorted to using many different names for their wares. Products

claiming various Eurycoma longifolia extract ratios of 1:20, 1:50, 1:100, and 1:200 are sold.

Traditionally Eurycoma longifolia is extracted with water and not ethanol. However, the use of

selling Eurycoma longifolia extract based on extraction ratio may be confusing and is not easily

verifiable.

In expectation of a competitive edge, some manufacturers are claiming standardization of

their extract based on specific ingredients. Alleged standards / markers are the glycosaponin

content (3545%) and eurycomanone (>2%). While eurycomanone is one of many quassinoids

in Eurycoma longifolia, saponins, known in ethnobotany primarily as fish poison played no role

in the academic research on the plant.

A large number of Malaysian Eurycoma longifolia products (36 out of 100) have been

shown to be contaminated with mercurybeyond legally permitted limits.

Herbal Nutrition

Increase strength of the body. Help to stimulate the production of testosterone that is one of the important hormones for

male.

Help to increase the blood rate and body metabolism.
http://en.wikipedia.org/wiki/Sildenafilhttp://en.wikipedia.org/wiki/Citratehttp://en.wikipedia.org/wiki/Ethanolhttp://en.wikipedia.org/wiki/Glycosaponinhttp://en.wikipedia.org/w/index.php?title=Eurycomanone&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Quassinoids&action=edit&redlink=1http://en.wikipedia.org/wiki/Mercury_%28element%29http://en.wikipedia.org/wiki/Mercury_%28element%29http://en.wikipedia.org/w/index.php?title=Quassinoids&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Eurycomanone&action=edit&redlink=1http://en.wikipedia.org/wiki/Glycosaponinhttp://en.wikipedia.org/wiki/Ethanolhttp://en.wikipedia.org/wiki/Citratehttp://en.wikipedia.org/wiki/Sildenafil


36/44



QUESTION (b) (ii) Designing a Logo


37/44



FURTHER

EXPLORATION

(Polygonal Buildings)


38/44



1. University of Economics and Business, Vienna

The new Library & Learning Center rises as a polygonal block from the centre of the new

University campus. The LLCs design takes the form of a cube with both inclined and straight

edges. The straight lines of the buildings exterior separate as they move inward, becoming

curvilinear and fluid to generate a free-formed interior canyon that serves as the central public

plaza of the centre. All the other facilities of the LLC are housed within a single volume that also

divides, becoming two separate ribbons that wind around each other to enclose this glazed

gathering space.

The Center comprises a Learning Center with workplaces, lounges and cloakrooms, library, a

language laboratory, training classrooms, administration offices, study services and central

supporting services, copy shop, book shop, data center, cafeteria, event area, clubroom and

auditorium.

Vienna, Austria 2008 2012 28000 m2 Gross Area: 42000 m

Length: 136m Width: 76m Height: 30m (5 Floors) Zaha Hadid with Patrik Schumacher


39/44



2. Pittman Dowell Residence, Los Angeles

The project is a residence for two artists. Located 15 miles north of Los Angeles at the

edge of Angeles forest, the site encompasses 6 acres of land originally planned as a hillside

subdivision of houses designed by Richard Neutra. Three level pads were created but only one

house was built, the 1952 Serulnic Residence. The current owners have over the years developed

an extensive desert garden and outdoor pavilion on one of the unbuilt pads. The new residence,

to be constructed on the last level area, is circumscribed by the sole winding road which ends at

the Serulnic house.

Five decades after the original house was constructed in this remote area, the city has

grown around it and with it the visual and physical context has changed. In a similar way, the

evolving contemporary needs of the artists required a new relationship between building and

landscape that is more urban and contained. Inspired by geometric arrangements of interlocking

polygons, the new residence takes the form of a heptagonal figure whose purity is confounded by

a series of intersecting diagonal slices though space.

Los Angeles, USA Residential - Houses Micheal Maltzan Architecture 3200 SF
http://architecturelab.net/keyword/los-angeles/http://architecturelab.net/keyword/usa/http://architecturelab.net/keyword/residential/http://architecturelab.net/keyword/houses/http://architecturelab.net/keyword/michael-maltzan-architecture/http://architecturelab.net/keyword/michael-maltzan-architecture/http://architecturelab.net/keyword/houses/http://architecturelab.net/keyword/residential/http://architecturelab.net/keyword/usa/http://architecturelab.net/keyword/los-angeles/


40/44



3. Casa da Musica, Porto

The Casa da Musica is situated on a travertine plaza, between the city's historic quarter

and a working-class neighborhood, adjacent to the Rotunda da Boavista. The square is no longer

a mere hinge between the old and the new Porto, but becomes a positive encounter of two

different models of the city. The chiseled sculptural form of the white concrete shell houses the

main 1,300 seat concert hall, a small 350 seat hall, rehearsal rooms, and recording studios for the

Oporto National Orchestra.

A terrace carved out of the sloping roofline and huge cut-out in the concrete skin

connects the building to city. Stairs lead from the ground level plaza to the foyer where a second

staircase continues to the Main Hall and the different levels above. Heavy concrete beams criss-

cross the huge light well above. The main auditorium, shaped like a simple shoebox, is enclosed

at both ends by two layers of corrugated glass walls. The glass, corrugated for optimal

acoustics and sheer beauty, brings diffused daylight into the auditorium. The structural heart of

the building is formed by four massive walls that extend from the base to the roof and connect

the tilted external walls with the core of the structure.

Porto, Portugal 22.000 square meters 2005 Concert Hall Rem Koolhaas and Ellen van Loon


41/44



CONCLUSION


42/44



CONCLUSION

Polygons tend to be studied in the first few years of school, as an introduction to basic

geometry and mathematics. But after doing research, answering questions, completing table and

some problem solving, I found that the usage of polygons is important in our daily life.

It is not just widely used in fashion design but also in other fields especially in building

of modern structures. The triangle, for instance, is often used in construction because its shape

makes it comparatively strong. The use of the polygon shape reduces the quantity of materials

needed to make a structure, so essentially reduces costs and maximizes profits in a business

environment. Another polygon is the rectangle. The rectangle is used in a number of applications,

due to the fact our field of vision broadly consists of a rectangle shape. For instance, most

televisions are rectangles to allow for easy and comfortable viewing. The same can be said for

photo frames and mobile phones screens.

In conclusion, polygon is a daily life necessity. Without it, mans creativity will be

limited. Therefore, we should be thankful of the people who contribute in the idea of polygon.


43/44



REFLECTION


44/44


REFLECTION

While I conducting this project, a lot of information that I found. I have learnt how

polygons appear in our daily life.

Apart from that, this project encourages the student to work together and share

their knowledge. It is also encourage student to gather information from the internet, improve

thinking skills and promote effective mathematical communication.

Not only that, I had learned some moral values that I practice. This project had taught me

to responsible on the works that are given to me to be completed. This project also had made me

felt more confidence to do works and not to give easily when we could not find the solution for

the question. I also learned to be more discipline on time, which I was given about a month to

complete this project and pass up to my teacher just in time. I also enjoy doing this project I

spend my time with friends to complete this project and it had tighten our friendship.

Last but not least, I proposed this project should be continue because it brings a lot

of moral value to the student and also test the students understanding in Additional Mathematics.

95055934 Add Math Project Work 2012

Documents

Transcript of 95055934 Add Math Project Work 2012