A generalization of Pythagorean triples for desirable quadrilaterals

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.