If you're allowed to move out of the plane of the square, then there are plenty of solutions. E.g., a square pyramid with edges 1,1,1,1,2,2,2,2. And there are almost certainly lots of less trivial (i.e., unsymmetric) solutions, R. On Fri, 29 Apr 2005, Daniel Asimov wrote:

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?

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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?

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