A generalization of Pythagorean triples for desirable quadrilaterals

Moshe Stupel; Avi(Berman) Siegler; Jay Jahangiri

Moshe Stupel “Shaanan" and "Gordon” - Academic College , Haifa, Israel
Avi(Berman) Siegler “Shaanan”-Academic College, Haifa, Israel
Jay Jahangiri Kent State University, Burton, Ohio, U.S.A.

Keywords: Pythagorean Triples, Desirable Quadrilaterals, Diophantine equations, Ptolemy's Theorem, Heronian Triangles.

Abstract

We explore the generalization of famous Pythagorean triples (a, b, c) for triangles to Pythagorean quadruples (a, b, c, d) for desirable quadrilaterals. Using number theory and geometrical techniques including Diophantine equations and Ptolemy’s Theorem, we show that there are infinite number of such quadrilaterals with specific relations between their sides and diagonals. We conclude our paper with an open question for further investigation.

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