In Pentallipse, Chandler West noticed that given an ellipse, if we were to choose 5 points which are equally spaced out around the perimeter, then the area of the pentagon is independent of the starting point.
He reached this conclusion by randomly testing starting points, but had difficulty evaluating the integrals.
How can we prove that this statement is true?
In the comments below, it is stated that this conjecture is actually not true. The ellipse was small enough, and too close to a circle, and the observation was within limits of experimental error.