About 1500 years ago, Aryabhatta had calculated the value of pi acur-ately.
Today, the ratio between the diameter and the circumference of a circle is called pi. Earlier, the measurement was estimated as the square root of 10. The first number of the product of one number, multiplied by itself becomes the square root. e.g. 2 x 2 = 4. Hence, 2 is the square root of 4. However, although it is difficult to give the right value of the square root of 10, yet, for calculation, it is important to know the nearest value. Aryabhatta puts this as:
Chaturadhikam Shatmashtagunam
Dwashashtisthta Sahsranam
Ayutdvayanishkambhyasanno
Vrittaparinahaha.
?(Aryabhattiya-10)
If the diameter of a circle is 20,000, then its circumference will be 62,832.
Aryabhatta does not consider this value as pure and exact, but approximate. This shows how insistent he was about truth.
Abul Fazal, a minister in Akbar'scourt wrote about the incidents of his time in his Ain-i-Akbari. He writes that the Greeks did not know that the Hindus had found out the mysterious relationship between the diameter and the circumference of a circle. Aryabhatta is supposed to be the first man to talk about the value of pi.
Trigonometry
Bodhayan'stheorem is the basis of trigonometry. Hence, the principles of trigonometry have naturally been given in the Shulbasootra. India'sjya and Kotijya became sine and cosine on going to the West. Actually, the word jya has come from a bowstring. In the picture that appears below, CA is like a half circle or bow and AP is like its string (jya). BP has been called kotijya. The Indian scholars had the knowledge to work out the value of kotijya (BP) and jya(AP) from the radius of the circle. If we assume angel ABP to be Q then Aryabhatta had calculated the value of jya and kotijya according to the angle Q. Aryabhatta said that the value of AP was trijya (BA) x jya (Q) and the value of RA (BP) was trijya (BA) x kotijya (Q). According to today'strigonometry, it is written as:
Aryabhatta found out the value of sine for the various angles, from O? to 90? and made a table for it too. There is a very interesting question in Bhaskaracharya'sLeelavati. Two monkeys are sitting on a tree which is 2,000 inches high (DB). About 4,000 inches away, there is a well (C). One monkey climbs down from the tree and goes to the well. The other monkey climbs to a set height (A) and jumps straight into the well. If the distance covered by the two monkeys is the same (DB + BC = DA + AC), then how high did the other monkey jump? Or how much is AD? This question definitely belongs to trigonometry and the distance covered comes out to be 5,000 inches. It is quite clear that Bhaskaracharya has described all the principles of trigonometry in Leelavati.
In the 4th part of his book Siddhant Shiromani, on astrological calculations, Bhaskaracharya has used differentiation to find out the speed of a planet. This part of mathematics, i.e. calculus, is the basis of modern science and technology. Liebatanis and Newton are considered fathers of calculus. Five hundred years before these two, Bhaskaracharya had used calculus to find the speed of the planets. Thus, we know about Indian superiority in the field of mathematics.
(This book is available with Ocean Books (P) Ltd, 4/19 Asaf Ali Road, New Delhi-110 002.)
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