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. --Joshua Zucker