Talk:Chakravala method

Mathematics Stub‑class Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Stub	This article has been rated as Stub-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-priority on the project's priority scale.

India Unassessed

	India portal This article is within the scope of WikiProject India, which aims to improve Wikipedia's coverage of India-related topics. If you would like to participate, please visit the project page.IndiaWikipedia:WikiProject IndiaTemplate:WikiProject IndiaIndia
???	This article has not yet received a rating on Wikipedia's content assessment scale.
???	This article has not yet received a rating on the project's importance scale.

Details

Would be great if someone could add some actual details about how this method works - especially as the article claims it is very simple. Gandalf61 08:16, 14 April 2006 (UTC)[reply]

I just added an "example", except that it's way too long, and I gave up before the answer was actually reached, because it's just so tedious. (Simple, but tedious.) If someone adds a proof that this method actually works, without any ad-hoc final steps or handwaving, I might add an implementation in C; but if we can't prove that it will terminate, there's not much point in pursuing that route. --Quuxplusone 22:48, 4 December 2006 (UTC)[reply]

It looks as if the is a little "bait and switch" between 61 and 67, as well as being unclear whether the 61 case was solved in the 7th, 9th or 12th centuries. --Rumping (talk) 15:03, 14 August 2008 (UTC)[reply]

===

I'm an algorithmist, not a number-theoretician, but most NT's I've spoken to agree with me that the chakravala is easiest viewed (and thus implemented) as a special type of CF (continued fraction).

The classical CF method (aka "English method") of solving Pell's equation involves an RCF (Regular Continued Fraction).

The chakravala corresponds (in CF terms) to the NSCF (Nearest-Square Continued Fraction).

An Indian mathematician named A.A.K. Ayyangar noticed this in the 1930's, but his work remains relatively unknown (Selenius cites AAK's results but nevertheless manages to claim credit for himself for unravelling the "true nature of chakravala").

If you have an algorithm for RCF it is easily adapted to yield NSCF, and also to get another variant called NICF (Nearest-Integer CF). Both NSCF and NICF are optimal CF's (ie: are the shortest-length CF's possible).

A friend of mine hosts a Number Theory website and we've co-written some papers on this. I'll come back with links when I can find them.

DeadHead52 (talk) 11:32, 12 September 2008 (UTC)[reply]

=