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Rebesques · #3 June 6th, 2007, 06:51 PM

Quote:

. It's not as formal as it could be, but I'm not a pure mathematician by a long way.

Don't be so humble, I think the proof is really good.

Now, about my attempt for 1. Consider the square to be ranging from -2 to 2 on every axis. The sequence of centers then satifies $||{\bf s}_{m+1}-{\bf s}_m||\leq \sqrt{2}\left(\frac{1}{2}+\ldots+\frac{1}{2^m}\right)\leq \frac{\sqrt{2}}{2}$ , so it is a Cauchy sequence.

For 3, induction gives an answer, but I don't like that kind of proof

Let me look if I can find something better.

For 2, I am at a loss

Hacker's love for algebra has ruined him!!