Square Pyramid: Underlying Anatomy

From Tim Brezinski

Indiana Puzzle Quilt

This applet was inspired by a quilt square my mother-in-law made. It provides a nice way of visualizing the  the sum of an infinite geometric series.
Check out the pattern in some real quilts, too!

Update 1/5/2017: See the Snail's Trail Quilt Square

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.)

Introduction to Area Under a Curve

In this applet from the GeoGebra Calculus Applets Project, you enter a function and position endpoints to see what the value of the integral is.

The Area Function

This applet from the GeoGebra Calculus Applets Project provides a way to explore the area function. The default integrand can be changed by right-clicking on the curve.

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.