## Aryabhata (476 - 550)

Aryabhata was only 23 when he completed his great work the *Aryabhatiya* in 499. Another work, the *Aryabhatasiddhanta*, is sadly lost. He was born near to the present day city of Patna in Northern India.

The *Aryabhatiya* is a summary of the mathematical knowledge of the day written in a very individual way - you might not recognise it as a mathematical book as it was written entirely in verse and comes without any proofs

Some of the verse is not consistent and people argue that some sections were added at a later date. It was certainly used by later Indian mathematicians and through its passage to Iran and beyond much influenced later Islamic mathematics.

Much of the *Aryabhatiya* is concerned with astronomy. Aryabhata realised that planetary motion was elliptic and that the earth rotates around an axis. Later on people who thought this was wrong edited it from the text, saving Aryabhata from what they presumed was a stupid error!

He correctly predicted solar and lunar eclipses and suggested that the light of the moon and planets was due to reflected sunlight. The first Indian satellite, launched in 1975, was named in his honour.

Aryabhata is also important for being one of the first to use a decimal number system. It worked something like this.

The 33 consonants of the Indian alphabet represented 1, 2 ,3 …, 25, 30, 40, 50, 60, 70, 80, 90, 100. Higher numbers were denoted by using these consonants followed by a vowel to obtain up to 10 to the power 18.

This system would not work unless zero and an idea of place value were used and we can perhaps credit him with their first use.

Aryabhata probably also gave the most accurate ancient measure of ‘pi’, something he seems to have worked out independently of Greek thinking.

He gave us the first table of sines, introduced versine into trigonometry and was one of the first to use algebra.

He gave the correct formulas for the area of a triangle and a circle, but his formulas for the volumes of a sphere and pyramid were wrong. This may be a fault of translation.

He also gives the circumference of the earth as 62832 miles, a remarkably accurate figure for the time.