Points at Rational Distance from the Vertices of a Square

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dc.contributor.advisorMorris, Walter D.
dc.contributor.authorSadeq, Joseph G
dc.creatorSadeq, Joseph G
dc.date2015-04-24
dc.date.accessioned2015-08-19T12:43:28Z
dc.date.available2015-08-19T12:43:28Z
dc.date.issued2015-08-19
dc.description.abstractGuy 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.
dc.identifier.urihttps://hdl.handle.net/1920/9760
dc.language.isoen
dc.subjectRational distance
dc.subjectDiophantine equations
dc.subjectSquare
dc.subjectNumber theory
dc.titlePoints at Rational Distance from the Vertices of a Square
dc.typeThesis
thesis.degree.disciplineMathematics
thesis.degree.grantorGeorge Mason University
thesis.degree.levelMaster's
thesis.degree.nameMaster of Science in Mathematics

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