I heard this question in the immediately equivalent version: < Is there a point in the plane at rational distances from each corner of a unit square?
My former thesis advisor, Moe Hirsch, has remarked, "If we don't know that, we don't know *anything*!" Here's a wider class of questions: Suppose we have a planar unit square in R^n for any n >= 2. Then is there a point of R^n at rational distance from each corner of the square? And if that fails: Suppose we have a planar unit square in Hilbert space H = {f: Z+ -> R : sum of all f(k)^2 < oo }. Then is there a point of H at rational distance from each corner of the square? (Here d(f,g) = sum of all (f(k)-g(k))^2.) --Dan ----------------------------------------------------------------- Richard Guy writes: << What we'd REALLY like to know is: Is there a point at integer distances from each corner of a square with integer edge?