From Random Polygon to Ellipse

Here is a fascinating and quite unexpected result from Shape Analysis.

I came across it at Matthen's blog which is great resource for visualising simple but intriguing mathematical results.

"Draw some random points on a piece of paper and join them up to make a random polygon. Find all the midpoints and connect them up to give a new shape, and repeat. The resulting shape will get smaller and smaller, and will tend towards an ellipse".

The visualisation is here and the paper demonstrating the result is here.