Marion's Theorem
Marion's theorem describes a property of triangles discovered through geometric exploration using dynamic mathematics software, and was formalized by the German-American mathematician Marion Ilse Walter in 1994.
The original formulation of the theorem was as follows:
Let be any triangle. Trisect each side so that has and as two trisection points, and similarly for the other two sides. Draw the line segments and . These segments define an hexagonal region in the middle of triangle . Then the area of the hexagonal region is the area of triangle .
The following applet contains a simplified statement of the theorem, but allows you to interactively trace the steps of the original construction and the numerical investigation of the result.
A special case of Marion's theorem applied to equilateral triangles was included in the first problem of the 1995 Scientific High School graduation exam in Italy.