22 June 2008

Aryabhata and Ptolemy

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


Pradeep Sinha said...

I would like to know more and read you books but online stores in India do not seem to carry them. Booksatbahri took payment and returned it saying that the book is not in stock. Can you please help by letting me know where these books could be available for purchase.

CKR said...

Sorry for this delayed response. I hardly ever visit this blog anymore. Check out my blog at http://ckraju.net/blog and my new books at http://ckraju.net. As for books, the Cultural Foundations of Mathematics book is available from Pearson, India, or local booksellers. (Let me know if it is out of print.) Another book "Is Science Western in Origin?" is available from Daanish Books, New Delhi or Other India Bookstore, Goa. I am making my latest book Euclid and Jesus available in India shortly.