Talk:Arithmetic-geometric mean: Difference between revisions
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:+1 on a and b. --[[User:Mwn3d|Mwn3d]] 19:11, 7 February 2012 (UTC)
Of possible interest: [http://oeis.org/A096427] —[[User:Sonia|Sonia]] 20:48, 9 February 2012 (UTC)
==On Using The Arithmetric Geometric Mean to Calculate Pi==
I have included examples of using the agm to calculate Pi:
http://rosettacode.org/wiki/Pi#C.2B.2B
http://rosettacode.org/wiki/Pi#using_agm
Proof and details of the algorithm used are described:
http://mathdl.maa.org/images/upload_library/22/Ford/Almkvist-Berndt585-608.pdf
The paper begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. From this section one should remeber equation (1) which defines c. Read through to Theorem 5 (derived from Theorems 3&4). If you have remembered the definition of c this should remind you of the above implementations.
The paper goes on to prove Theorem 5, though one couls argue that the success of the above implementations is proof. It then procedes to show how the agm may be used to calculate length of the perimeter of an elipse without differential calculus, which was the origional intent (perhaps another task), but really we are only interested in Pi.
--[[User:Nigel Galloway|Nigel Galloway]] 14:26, 29 March 2012 (UTC)
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