Mahavira (mathematician)

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Mahavira was a 9th century Indian mathematician from Gulbarga who asserted that the square root of a negative number did not exist. He gave the sum of a series whose terms are squares of an arithmetical progression and empirical rules for area and perimeter of an ellipse. He was patronised by the great Rashtrakuta king Amoghavarsha. Mahavira was the author of Ganit Saar Sangraha. He separated Astrology from Mathematics. He expounded on the same subjects on which Aryabhata and Bramhagupta contended, but he expressed them more clearly. He is highly respected among Indian Mathematicians, because of his establishment of terminology for concepts such as equilateral, and isosceles triangle; rhombus; circle and semi-circle. Mahavira's eminence spread in all South India and his books proved inspirational to other Mathematicians in Southern India.

Contents

Mahavira solved higher order equations of n degree of the forms:

\ ax^n = q

And

a \frac{x^n - 1}{x - 1} = p

Mahavira expressed characteristics of a cyclic quadrilateral, like Brahmagupta did previously. He also established equations for the sides and diagonal of Cyclic Quadrilateral.

If sides of Cyclic Quadrilateral are a,b,c,d and its diagonals are x and y while

\ x = \sqrt {\frac{ad + bc}{ab + cd} (ac + bd)}

And

y = \sqrt {\frac{ab + cd}{ad + bc} (ac + bd)}

Then, \ xy = ac + bd

v • d • e
Indian mathematics
Mathematicians Achyuta Pisharati · Apastamba · Aryabhata · Aryabhata II · Bhāskara I · Bhāskara II · Baudhayana · Brahmagupta · Jyesthadeva · Katyayana · Madhava · Mahavira · Manava · Melpathur Narayana Bhattathiri · Nilakantha Somayaji · Parameshvara · Pingala · Sripati · Sridhara · Varahamihira · Virasena
Treatises Aryabhatiya · Bakhshali manuscript · Paulisa Siddhanta · Paitamaha Siddhanta · Romaka Siddhanta · Surya Siddhanta · Śulba Sūtras · Vasishtha Siddhanta · Yavanajataka
Centers Kerala
Influences Babylonian mathematics · Greek Mathematics · Chinese mathematics
Influenced Islamic mathematics · Chinese mathematics
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Retrieved from "http://en.wikipedia.org/wiki/Mahavira_%28mathematician%29"
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