Regular Polygon Maker
If you increase the number of sides in a regular polygon, it soon starts to resemble a circle.
This Demonstration introduces the idea of limits. Would it be a circle if the number of sides were infinite?
A tooltip shows the area of the polygons, which approaches as the number of sides increases.
(This example was used in the author’s TEDGlobal 2010 talk "Stop Teaching Calculating, Start Teaching Math".)