Eisenstein triple


Similar to a Pythagorean triple, an Eisenstein triple is a set of integers which are the lengths of the sides of a triangle where one of the angles is 60 degrees.

Triangles with an angle of 60°

Triangles with an angle of 60° are a special case of the Law of Cosines:
When the lengths of the sides are integers, the values form a set known as an Eisenstein triple.
Examples of Eisenstein triples include:
Side aSide bSide c
387
587
52119
74037

Triangles with an angle of 120°

A similar special case of the Law of Cosines relates the sides of a triangle with an angle of 120 degrees:
Examples of such triangles include:
Side aSide bSide c
357
7813
51619