Indian mathematicians and their contribution to the field of mathematics

Mathematics in India

• India had a glorious past in every walks of knowledge.

• However, the Indian contribution to the field of mathematics are not so well known.

• Mathematics took its birth in India before 200 BC,ie the Shulba period.

• The sulba sutras were developed during Indus valley civilization.

• There were seven famous Sulbakars (mathematicians of indus valley civilization) among which Baudhyana was the most famous. His works were mainly based on geometry and include enunciation of today’s Pythagoras theorem and obtaining square root of 2 correctly upto 5 decimals.

• The Pythagoras Theorem in Sulbha sutra.The Sutra Says:

• “dirghasyaksanaya rajjuh parsvamani, tiryadam mani,Cha yatprthagbhuta Kurutastadubhayan karoti”.

• A Rope stretched along the length of the diagonal (hypotenuse) produces an area which the vertical and horizontal sides make together.Here DB is the hypotenuse.

Classic period {400-1500}

• This period is often known as the golden age of Indian Mathematics. This period saw mathematicians such as Aryabhata, Varahamihira, Brahmagupta, Bhaskara I, Mahavira, and Bhaskara II give broader and clearer shape to many branches of mathematics. Their contributions would spread to Asia, the Middle East, and eventually to Europe.

• As explained earlier, the main texts were composed in Sanskrit verse, and were followed by prose commentaries.

• This saga of people who contributed much to mathematics ended with Madhava of Sangamagrama from kerala when his school was destroyed in the 16th centuary

aryabhatta• The most celebrated mathematician during

the classic period.Many honours have been placed on him and also he is the birthplace of many mathematical theorems functions etc.

• He was born in 476 AD with many controversy over his birth place;some say he was born in Kodungallor,Kerala some atribute it to Taregna,Bihar.

• He is known for his famous treatise Aryabhatiya written in 499 AD when he was 23

• Credits confered to him include value of pi, earth’s rotation time period,extraction of cube root of a number, indeterminate equations,trigonometry etc

Aryabhatta and PI• Aryabhata worked on the approximation

for pi , and may have come to the conclusion that  is irrational.

• caturadhikam satamastagunam dvasastistathasahasranamayutadvayaviskambhasyasanno vrttaparinahah."Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached." [15]

• This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures.

• After Aryabhatiya was translated into Arabic this approximation was mentioned in Al-Khwarizmi's book on algebra.

Aryabhatta and TRIGONOMETRY,

INDETERMINATE EQUATION AND ALGEBRA

•  Aryabhata gives the area of a triangle as tribhujasya phalashariram samadalakoti

bhujardhasamvargahthat translates to: "for a triangle, the reult of a perpendicular with the half-side is the area”.

• Aryabhata discussed the concept of sine in his work by the name of ardha-jya, which literally means "half-chord”.

• Today known as diophantine equation; the indeterminate equation was always discussed in Aryabhatiya .

• His method of soving was as follows:-N=ax+c=by=d or ax-by=k• His contribution to algebra was also

sophisticatedly important.

bhaskarA 1• He was born at Bori, in Parbhani district of

Maharashtra state in India in 7th century.• He was the first to write Hindu-Arabic

numerals and with zero with a circle.• He was an exponent of Aryabhatta, named

Aryabhatiyabhasya.• He gave importance to sine function in

Aryabhatiyabhasya.• He represented number using nonliving and

living thingFor eg:- 1 was for moon , 2 was for eyes,wings etc, 5 was for the senses of humans.• His famous books include Laghubhaskariya

and Mahabhaskariya.• Not to be mistaken for Bhaskara II of 12th

centuary

• He was an astrologer manly but was also a mathematician.

• He was born in 6th centuary in Ujjain and considered to be one of the nine jems of Vikramaditya II

• The trigonometric formulas

• His famous work is Panchasidanthika

varahamihira

• Bramagupta belonged to the city of ujjain .• Regarded as the man who used zero as a

number, negative numbers.• The statement a negative integer multiplied

by a negative integer give a positive integer and many other fundamental operation first appeared in his treatise Bhramasphutasiddhanta. But how he came to the conclusion was unknown.

• He gave basic idea to the d-quadratic method of solving.

• The following identity was attributed to him x2 - y2 = (x + y)(x - y)• He gave some information about what is

today known as Pythagorean triplets.• He is also known to give a touch to today’s

Pell equation

brahmagupta

Brahmagupta and cyclic quadilateral

• He is famous for the theorem which he gave for a cyclic quadilateral. Today this is known as Brahmaputra’s formula.

• The area of a quadilateral scribed in a circle is the square root from the product of the halves of the sums of the sides diminished by [each] side of the quadrilateral

where

• He was a jain Mathematician• His celebrated work was

Ganithasarangraha.• He showed ability in quadratic

equations, indeterminate equations.

mahavira

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govindaswamin

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SRIDHARAARYABHATTA II

SRIPATI

BHASKARACHARYA

MADHAVA