Mathematics in Ancient and Medieval India c8.s2.1

c8.s2.1

Historians have devoted much attention to the efforts of the old mathematicians to arrive at approximations to the value of the ratio between the circumference and the diameter of a circle. There is evidence¹ that the ancient Egyptians and old Babylonians had values such as 3.1604 and 3.125, the commonest practice in ancient civilisations was to take the ratio simply as 3. The ancient Indians also used the values varying from 3.1416(=3927/1250), 3.14136(=21600/6876)....., 3.14285(=22/7)........., 3.16227........, 3.0883........, 3.0885……., and 3. Of these the nearest approximation (3.1416) to the correct value is given by Āryabhaṭa I in the 5th century A. D. None of these values were determined from the ratio of the circumference of the earth to its diameter. On the other hand, they used the π values for determining the earth’s diameter from its circumference.¹ Nīlakaṇṭha ( 1500 A. D. ) gave the value 355/113 in his *Tantrasaṃgraha* ( TSS 188, ch. 2, vs 7 ). Mādhava ( 1400 A. D. ) used the circumference of a circle as 2827433388233 when its diameter was 9 × 10¹¹, which gives π = 3 14159265359 correct to 11 places of decimals.