Visualizing Radian Measure

Ted Coe's Unwrapping a Circle applet on GeoGebra Tube is a visually powerful way of demonstrating what a radian is. I've also posted a slight modification of the applet optimized for use as a demonstration.

Constructing the Area of a Circle

A beautifully designed applet that walks you through finding the area of a circle by dividing it up into sectors and rearranging them to form a shape which becomes a rectangle as the number of sectors goes to infinity. I recommend using it in conjunction with Steven Strogatz's fabulous article, "Take it to the Limit". (If you like this, you might also like this applet which approaches the same problem in a slightly different way.)

Turning a Circle into a Rectangle

After reading Steven Strogatz's column Take It to the Limit, I developed this animation (using GeoGebra) of Strogatz's diagram which shows why the formula for the area of circle is what it is, and also provides an approximation for π.