Japanese Sangaku mathematics has a rich history of geometric theorems and problems. The equal incircles theorem is an illustrative example. Consider the incircle

of radius

of any triangle (each side of the triangle is tangent to the circle) and the extended line

along one side of the triangle. Construct a triangle with base common to

and an incircle of radius

on either side of the triangle. Continue this process on either side of the group of triangles until

triangles are constructed,

. The incircle of the triangle formed by the combination of any

,

, adjacent triangles taken from the group of

individual triangles has the same radius as the incircle of the triangle formed by any other

adjacent triangles.