The Mathematical Grotto

This animation of little Escher plane-filling figures is by Nancy Lopez.

A Topological Java Game:

Here is a interesting maze game developed by Jeff Weeks. This game is an excellent way for kids and adults to learn about the strange topological properties that surfaces can have. It is played on a torus (i.e., a surface that is topologically equivalent to the surface of a donut) or on a Klein bottle. If you find the game interesting then you can go to Jeff Weeks' page. A 2-week Shape of Space unit for middle school math classes uses classroom games and activities, the Torus and Klein Bottle Games from Jeff's web site, and a video to expand kids' concept of space. You can contact Jeff directly at:

Virtual Cube

You might as well be searching through a maze if you play with The Cube. This marvellous java model is created by Song Li and David Liu. This cube is an interesting way to teach students about the actions of finite groups on sets. The group action is accessible to the student but non-trivial to solve. Concepts such as orbits, commutativity, the order of an element, and other ideas can easily be explained using this model.

Animation List:

• Animated proof of the Pythagorean Theorem
• Checking out the chirality of the figure eight knot
• Approximating an integral with a riemann sum
• Approximating the tangent to a curve using secants

The next three animated gifs show random dives into the famous Mandelbrot set.

• A dive into the Mandelbrot set - 1.
• A dive into the Mandelbrot set - 2.
• A dive into the Mandelbrot set - 3.

• An animation of the Penrose Triangle.

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