# 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°

An Eisenstein triple

Triangles with an angle of 60° are a special case of the Law of Cosines:[1][2][3]

${\displaystyle c^{2}=a^{2}-ab+b^{2}.}$

When the lengths of the sides are integers, the values form a set known as an Eisenstein triple.[4]

Examples of Eisenstein triples include:[5]

Side a Side b Side c
3 8 7
5 8 7
5 21 19
7 40 37

## Triangles with an angle of 120°

Triangle with 120° angle and integer sides

A similar special case of the Law of Cosines relates the sides of a triangle with an angle of 120 degrees:

${\displaystyle c^{2}=a^{2}+ab+b^{2}.}$

Examples of such triangles include:[6]

Side a Side b Side c
3 5 7
7 8 13
5 16 19