aryabhatta

Contribution of Indian Mathematicians
                                                           

(1) Aryabhatta was born in 476 A.D. Kusumpur, India.He was the first in the line of great
mathematicians from the classical age of Indian Mathematics and Astronomy.

(2) His famous work are the” Aryabhatiya “and the”Arya‐siddhanta”.The Mathematical
part of the Aryabhatiya covers arithmetic. algebra, plane and spherical trigonometry.The
Arya‐siddhanta, a lot work on astronomical computation

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(3) Approximation of Pi: Aryabhata work on the approximation for pi (π) and may have
come to the conclusion that π is an irrational number.In the 2nd part of Aryabhatiya, he
writes the ratio of circumference to diameter is 3.1416.


(4) Aryabhata given the formula for area of a triangle .He also discussed the concept of
sine in his work by the name of ardhajya. If we use Aryabhata’s table & calculate the
value of sin300 which is 1719/3438=0.5.,the value is correct. His alphabetic code is
commonly known as the Aryabhata cipher.


(5) He was first person to say that Earth is spherical and it revolves around the sun.
(6) He gave the formula (a+b)2 =a2 + b2 + 2ab.
(7) He taught the method of solving the following problems:
1+2+3+…………+n = n(n+1)/2
12 + 22 + 32 +………+ n2 = n(n+1)(2n+1)/6
13 + 23 + 33 +…………..+ n3 = (n(n+1)/2)2
BRAHMAGUPT(598‐668 AD)

(1) Brahmagupta was born in 598 A.D.in Bhinmal city in the state of Rajasthan. He was a
mathematician and astronomer, who wrote many important works on mathematics and
astronomy. His best known work is the “Brahmasphuta‐siddhanta”, written in 628 AD in
Bhinmal.
(2) He was the first to use zero as a number. He gave rules to compute with zero.


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(3) He gave four methods of multiplication.
(4) He gave following formulae, used in G.P. series
a+ar+ar2
+ar3 +……….+arn‐1 =a(rn
 ‐1)/( r‐1)
(5) He gave the following formulae(Brahmagupta’s formula):
Area of a cyclic quadrilateral with side a,b,c,d =9(s‐a)(s‐b)(s‐c)(s‐d), where 2s= a+b+c+d.
Length of its diagonals=ට௕௖ା௔ௗ
௔௕ା௖ௗ (ac+bd), ට௔௕ା௖ௗ
௕௖ା௔ௗ (ac+bd).
BHASKARACHARYA  (1114‐1185 AD)

(1) He was born in Bijapur in modern Karnataka. He & his work represent a significant
contribution to mathematical & astronomical knowledge in the 12th century.
(2) His main work “Siddhanta Shiromani” is divided into four parts called Lilawati,
Bijaganit, Grahaganita and Goladhyaya. These four sections deal with arithmetic, algebra,
mathematics of planets and spheres respectively.
(3) He was the first to give that any number divided by zero gives infinity.


(4) He was written a lot about zero, surds, permutation and combination.
(5) He wrote,” The hundredth part of the circumference of a circle seems to be straight.
Our earth is a big sphere and that’s why it appears to be flat.”
(6) He gave the formulae like: sin(A±B)=sinAcosB ±  cosA sinB.
(7) He calculated derivatives of Trigonometric functions and formulae.

(8) He developed spherical trigonometry alongwith a number of other trigonometric
results.
(9) He explained solution of quadratic, cubic and quartic indeterminate equations.
(10) He developed a proof of Pythagoras Theorem by calculating the same area in two
different ways & these cancel out terms to get a2 + b2 = c
2.
(11) He gave first general method for finding the solution of the problem x
2 – ny2 = 1 (so
called Pell’s equation ).
(12) He gave solution of Diophantine equations of second order such as 61x2 + 1 = y
2..
RAMANUJAN (1887‐1920)
(1) Ramanujan was born on 22nd of December 1887 in Erode, Madras Presidency. He
made extraordinary contributions to mathematical analysis, number theory, infinite
series, and continued fractions.