Points at Rational Distance from the Vertices of a Square
Date
2015-08-19
Authors
Sadeq, Joseph G
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Abstract
Guy asks if there exists a point in the plane at rational distance to the corners of the unit square. Also known as the four-distance problem, we establish the equivalence of the problem to the existence of nontrivial solutions to a particular Pythagorean triple, from which we derive known conditions and establish new results. We then provide a generalization given by Barbara of the four-distance problem to regular polygons of unit side, in which a negative answer is almost always obtained.
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Keywords
Rational distance, Diophantine equations, Square, Number theory