How does Aryabhata's value of pi compare with Ptolemy's?
Date: Sat, 12 Jan 2008 19:12:36 +0500
Subject: Re: Aryabhata and Ptolemy
Dear Mr Smith,
Thank you for your interest in my article on Aryabhata.
Geometrical techniques for computing pi were used in India since the sulba sutra (-500 CE). In my book Cultural Foundations of Mathematics (more details at http://indiancalculus.info/ ) I argued that Aryabhata discarded geometrical techniques and shifted to an elegant numerical technique to compute pi. This is essentially the same as what is today known as Euler's method for solving ordinary differential equations. This technique was later used by the 14th c. Madhava to derive the value of pi accurately to ten decimal places. Using a continued fraction expansion gave 355/113 etc. as successive convergents, which were explicitly obtained.
In the same book I have also argued that the Almagest is an accretive text for which no unique author can be identified, and there is no evidence for any actual person by name Claudius Ptolemy. The knowledge contained in the available versions of the Almagest from after 9th c. is not reflected in the calendar reforms of the 4th through 6th centuries.
With good wishes,
C. K. Raju