On Tue, 5 Sep 2006, Joshua Zucker wrote:
On 9/4/06, N. J. A. Sloane <njas@research.att.com> wrote:
Many years ago i saw an abstract in the Oberwolfach Vortragsbuch entitled "Squares in Lake Michigan", which for a long time I thought proved theorems such as "any Jordan curve - or distorted circle in the plane - contains 4 points which are at the vertices of a square". But I never saw anything more about this, and began to doubt my memory. Just now I found the following on MathSciNet, so maybe it was not a dream:
Hi Neil and all, I was just reading Peter Winkler's book _Mathematical Puzzles_, and in it I saw the equivalent of "squares in lake michigan" as an unsolved puzzle. He says there are proofs that sufficiently smooth curves always contain a square, but no general proof that every Jordan curve contains a square.
I thought I saw an article in the popular press within the last year or two in which a mathematician noticed his table wobbling, and found that by rotating it he could get all 4 legs stable. So he investigated it and wound up proving that it's possible to do so for any surface. I'm not turning anything up on google, though. -J