Clifford A. Reiter and Jorge F. Sawyer, Generalized Perfect Parallelograms and Their Matrix Generators, JP Journal of Algebra, Number Theory and Applications, 16 1 (2010) 1-12.

Perfect parallelograms have edge lengths and diagonal lengths that are all positive integers. These generalize Pythagorean triples which are perfect rectangles. We consider the distribution of perfect parallelograms and show they satisfy a quadratic Diophantine equation. The solutions to that Diophantine equation can be generated by a finite collection of matrices that generalizes the matrix based tree of Pythagorean triples.

See Also: · Preprint of the manuscript. · [Abstract][Preprint] for related manuscript "Pursuing the Perfect Parallelepiped". · [Abstract][Preprint] for related manuscript "Matrix generation of the Diophantine Solution of 3 ≤ n ≤ 9 Squares that are Square". · [Abstract][Preprint] for related manuscript "Families of Nearly Perfect Parallelepipeds". · [Materials] for related manuscript "Perfect Parallelepipeds Exist".