Re: [math-fun] Games of Ramsey and van der Waerden

On Monday 30 October 2006 00:57, Daniel Asimov wrote:

A square is defined here as four *distinct* points of GxG -- P,Q,R,S -- such that the segments PQ, QR, RS, ST are of equal length, and the angles PQR, QRS, RSP, SQP are right. A square is determined by its set of vertices.

Oh -- and the metric used on GxG is just the cartesian product of that on G with itself, where G is a regular octagonal curve.

OK. Allow me to suggest that that's less natural than the different definition I proposed, because it seems freaky to consider {a1,c1,e1,g1} a square. But it's your game, so you get to choose the rules :-). -- g