Japanese theorem
From Wikipedia, the free encyclopedia
The Japanese theorem is the following theorem in geometry.
Let
- A1, A2, ... , An
be a cyclic polygon. The theorem states that no matter how we triangulate the polygon, the sum of inradii of triangles is constant.
Conversely, if the sum of inradii independent from the triangulation, then the polygon is cyclic. The Japanese theorem follows from the Carnot's theorem; it is a Sangaku problem.
[edit] External link
- Japanese theorem in Mathworld
- Japanese Theorem interactive demonstration at the C.a.R. website
