A Problem due to Steinhaus is the following: do there exists a point in the plane at rational distance from the corners of the unit square?
Please give me a reference if this problem is solved.
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4$\begingroup$ The problem is still open. Cf. mathworld.wolfram.com/RationalDistanceProblem.html $\endgroup$– Benjamin DickmanCommented Jun 4, 2018 at 16:33
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