# Visualization of 3D Mathematics

An ongoing project to provide visualization tools to students in multivariable calculus has led to a broader interest in the visualization of mathematics. Lately I have been particularly interested in the GeoWall, a system which uses polarized filters to display stereo images in three dimensions. As the name implies, GeoWalls have largely been used by Earth Scientists, and we are just starting to explore its potential in mathematics.

If you are specifically interested in course materials for multivariable calculus and vector analysis, follow the "Vector Calculus" link on the menu to the left. That page also includes a number of two-dimensional visualization tools.

### Standalone OpenGL applications

 stereoEversion is a minor fork of Michel McGuffin's sphereEversion program. It displays Thurston's eversion of the sphere, as shown in the movie Outside In. The version here includes a stereo mode for use with a GeoWall. Windows: stereoEversion.zip. Linux: stereoEversion.tar.gz. (Might compile on other platforms.) The Curved Spaces package by Jeff Weeks to display its images in a stereo mode. This program allows you to view and fly through flat, spherical and hyperbolic spaces. The package has been updated to include a passive 3D mode suitable for use with a GeoWall. You can download it at www.geometrygames.org.

### LiveGraphics3D Materials

The following materials were all created with LiveGraphics3D, a Java applet written by Martin Kraus. If you would like to develop similar materials, you can read this online preprint of an article Martin and I wrote to describe how to create visualizations with LiveGraphics3D

Clicking on any of the following links will open the applet in a new window. Please note: depending on your browser, operating system and/or window manager, you might have to move the window to the corner of your desktop and/or resize the window to stretch across both screens.

You can use the following controls:

• Click+Drag: rotate the image
• Shift+Click+Drag Up/Down: zoom in/out
• Home: reset the image
• Double Click: stop/restart the animation (if applicable)
• 's' key: cycle through normal mode, parallel stereo mode, and cross-fusion stereo modes.

Any of the "GeoWall" links will automatically start in parallel stereo mode.