Sequence of polygons 
Bisection of the diagonals of a pentagon
Instructions
Click on the vertices of the initial pentagon (blue dots) and drag them, observing the new pentagons constructed by bisecting their diagonals.
Note that the last pentagons in the app appear to have the shape of a star (possibly degenerated into a line segment or a point). In fact, the sequence of new pentagons always tends to pentagons with this shape. Why?
