----- Original Message ----- From: <dasimov@earthlink.net> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Wednesday, February 22, 2006 19:27 Subject: Re: [math-fun] (a1 + a2 + ...)^2 = a1^2 + a2^2 + ... = Pi^2/8
What would be really cool to see would be a *geometrical* proof of sum (1/n^2) = pi^2 / 6. That is, some object of volume pi^2 / 6 that can be partitioned into pieces of volume 1/n^2.
You might be interested in <http://www.pisquaredoversix.force9.co.uk/Tiling.htm>. BTW, before Clive found that, I had found another conjectured packing, using an algorithm slightly different from his. If interested, see <http://groups.google.com/group/sci.math/msg/d92d4a0ea46b4762> and other messages in that thread and its parent. Unfortunately this cannot (obviously) be considered to "be a *geometrical* proof of sum (1/n^2) = pi^2 / 6". Cheers, David