Subject: Re: [HM] Indian derivation of sine series
From: Kim Plofker (Kim_Plofker@Brown.edu)
Date: Mon Aug 07 2000 - 23:21:43 EDT
The crucial point is that the methods for the Madhava-Newton power
series for sine and versine go back to Madhava at the beginning of
the fifteenth century. His methods are described, and verses
attributed to him quoted, in several later works, but his own original
work on the subject has not survived on its own, as far as we now know.
The verse most commonly attributed to Madhava is not expository but
mnemonic, containing in katapayadi notation the first five
(non-unity) coefficients to multiply by the successive powers of the
arc in the sine series. (This is the famous "vidvams" verse.) It's
clear from the coefficients that Madhava knew the general rule for
the terms of the series.
Verses describing in detail how to compute the sine and versine values,
though, appear in later works. I can go into the whole question of
which verses thought to be composed by whom show up in which texts
when, but it is a rather messy issue and I hope the knowledge that
the series technique is quite confidently accepted to date back to
Madhava in the early 1400's will content you. If not, let me know.
With best wishes,
Kim Plofker
Department of the History of Mathematics
Brown University
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