Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Wikipedia attributes Leibniz's formula to Madhava of Sangamagrama, James Gregory and Gottfried Leibniz. But what were their proofs?

share|cite|improve this question
sorry about the format – Alex Nov 12 '12 at 3:15
@ Alex - I don't see a proof in the article on Madhava of Sangamagrama. Thanks for the other reference. I wish we had a reference that tied Gregory's proof down to a specific historical source. – Jonah Sinick Nov 12 '12 at 3:23… – Alex Nov 12 '12 at 3:26
up vote 2 down vote accepted

A good reference for this question is Ranjan Roy: The Discovery of the Series Formula for $\pi$ by Leibniz, Gregory and Nilakantha. Mathematics Magazine, Vol. 63, No. 5, December 1990, pp. 291-306. The article is reprinted in Berggren et al.: Pi: A Source Book.

Gregory did not publish his results on series, but he corresponded with John Collins in London from 1669 until his (Gregory's) death in 1675, and the arctan-formula is contained there. The correspondance was published by Turnbull in 1939.

In the title of his article, Ray has chosen to name Nilakantha rather than Madhava who lived a century earlier. The reason is that we do not have the original text of Madhava; while he is credited by Nilakantha, it is not clear if this also includes the arctan-formula.

share|cite|improve this answer
Thanks Per Manne! – Jonah Sinick Nov 14 '12 at 5:01
The article is available online here. – ShreevatsaR Feb 26 '14 at 2:10

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.