Monday, August 4, 2008

Mahavira (mathematician)

Writing in the 9th century (flourished c. 850), Jain mathematician Mahavira stated rules for operations with zero, although he thought that division by zero left a number unchanged.

He was born Gulbarga, Karnataka in 9th-century. He was patronised by the great Rashtrakuta king Amoghavarsha. He 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.

Mahavira was the author of Ganit Saar Sangraha. He separated Astrology from Mathematics. He expounded on the same subjects on which Aryabhata and Brahmagupta 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 semicircle. Mahavira's eminence spread in all South India and his books proved inspirational to other Mathematicians in Southern India.

The only known book by Mahavira is Ganita Sara Samgraha, dated 850 AD, which was designed as an updating of Brahmagupta's book. and was translated into Telugu language by Pavuluri Mallana as Saar Sangraha Ganitam.

This book consisted of nine chapters and included 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. There were many Indian mathematicians before the time of Mahavira but, perhaps surprisingly, their work on mathematics is always contained in texts which discuss other topics such as astronomy. The Ganita Sara Samgraha by Mahavira is the earliest Indian text which we possess which is devoted entirely to mathematics.

In the introduction to the work Mahavira paid tribute to the mathematicians whose work formed the basis of his book. These mathematicians included Aryabhata I, Bhaskara I, and Brahmagupta.

Mahavira writes in the book:-

"With the help of the accomplished holy sages, who are worthy to be worshipped by the lords of the world ... I glean from the great ocean of the knowledge of numbers a little of its essence, in the manner in which gems are picked from the sea, gold from the stony rock and the pearl from the oyster shell; and I give out according to the power of my intelligence, the Sara Samgraha, a small work on arithmetic, which is however not small in importance. "

The nine chapters of the Ganita Sara Samgraha are:
  1.  Terminology
  2. Arithmetical operations
  3. Operations involving fractions
  4. Miscellaneous operations
  5. Operations involving the rule of three
  6. Mixed operations
  7. Operations relating to the calculations of areas
  8. Operations relating to excavations
  9. Operations relating to shadows

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