Page 97 - Mathematics Class - XII

PROJECT 3

AIM
History and contributions of various Indian Mathematicians like Aryabhatta, Brahmagupta, Mahavira,
Bhaskaracharya, Srinivasa Ramanujan and many more, in the field of mathematics.

ARYABHATTA’S CONTRIBUTIONS
1. He was the first person who gave the accurate value of p up to four decimal places which is 3.1416, no other
person had achieved such achievement in that century.

2. Aryabhatta was the pioneer to introduce the concept of ‘Bijganita’ or Algebra.
3. Aryabhatta was the first person who invented the modern method of finding square root.

4. Aryabhatta was also the first person who gave the general integral solution of linear equations.

BRAHMAGUPTA’S CONTRIBUTIONS

1. In his Brahmasphutasiddhanta, Brahmagupta extensively dealt with the properties of cyclic quadrilateral
and trapezium and the relation between their sides, diagonals and area.
2. Aryabhatta had prepared the sine table. Brahmagupta, in his Khandakhadyaka stated a new method to find
out the intermediate sine values from the Aryabhatta’s sine table values. After one thousand years, Newton
(1642–1727) and other mathematicians rediscovered this theory by the name of “Theory of Interpolation”.

3. In addition to the Brahmasphutasiddhanta, Brahmagupta wrote a second work on mathematics and
astronomy which is the Khandakhadyaka written in 665 when he was 67 years old.
4. Another arithmetical result presented by Brahmagupta is his algorithm for computing square roots, which
is equivalent to the Newton-Raphson iterative formula.

5. Brahmagupta developed some algebraic notations and presented methods to solve quadratic equations. He
presented methods to solve indeterminate equations of the form ax + c = by.

MAHAVIRA’S CONTRIBUTIONS
1. In his Ganitasarasangraha, Mahavira was concerned with the properties of right-angled triangles, area and
circumference of ellipse, geometric progression series and so on.

2. He used his mathematical knowledge in various calculation on excavation and shadows.
3. Mahavira was a follower of the Jaina religion and was familiar with Jaina mathematics.

4. The only known book by Mahavira is Ganita Sara Samgraha (850 AD). It consists of nine chapters and
includes all mathematical knowledge of mid-ninth century India. It provides us with the bulk of knowledge
which we have of Jaina mathematics and it can be seen as in some sense providing an account of the work
of those who developed this mathematics.

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