featuring area coordinates, hey they're only natural
Marion Walter, mathematician
STATEMENT
If each side of an arbitrary triangle is trisected and lines are drawn to the opposite vertices, the area of the hexagon created in the middle is one-tenth the area of the original triangle.
A beautiful presentation. This theorem emphasizes the usefulness, daresay necessity, of trilinear coordinates.
More trilinear yet
Note: This mathworld article also mentions a generalization of Marion’s theorem sometimes known as Morgan’s theorem was found by Ryan Morgan, a sophomore at Patapsco High School in Baltimore (Morgan 1994).
