A pythagorean triangle with catheti and and hypotenuse is characterized by the well-known equation . However, this can also be formulated differently:
When inscribed into a circle with radius , a triangle with sides , and is pythagorean, if and only if .
Analogously, we call a quadrilateral with sides , , and , inscribed in a circle with radius , a pythagorean quadrilateral, if .
We further call a pythagorean quadrilateral a pythagorean lattice grid quadrilateral, if all four vertices are lattice grid points with the same distance from the origin (which then happens to be the centre of the circumcircle).
Let be the number of different pythagorean lattice grid quadrilaterals for which the radius of the circumcircle is . For example , , and .
Two of the pythagorean lattice grid quadrilaterals with are illustrated below: