# Computer graphics for teaching

This web page contains material for a presentation on some uses of computer-generated graphics in teaching mathematics.

## Maple examples

This group of examples consists of Maple worksheets. Apart from the last example they were contributed by Peter Dixon and Simon Willerton; some of Simon's material was inherited from Kirill Mackenzie. I have edited them to make bite-sized chunks in a uniform style, and added some documentation in places. Here are some further examples contributed by Kirill Mackenzie, which he has used in PMA340 and/or PMA441.

## Live3D examples

For my course on Groups and Symmetry, I produced many diagrams of Platonic solids and their symmetries. These are displayed using a freely available Java applet called LiveGraphics3D, which makes it possible to display the pictures in a browser, and zoom and rotate them using a mouse. (Maple also provides this functionality, but the viewer needs to have Maple installed on his/her machine, whereas LiveGraphics3D works with any Java-enabled browser.)
The pictures were generated using Mathematica rather than Maple. LiveGraphics3D is designed to take Mathematica output as its input, but it would not be too hard to write a routine to convert Maple output into the required format.

## Javascript examples

For my course on Algebraic Topology, I produced many animated diagrams of topological phenomena. These were generated using Mathematica, but Maple could have been used instead. Each frame of each animation was saved as a separate gif file, and I wrote Javascript code to control the animations (so that they can be run forwards or backwards, slowed down, set to repeat indefinitely, and so on).

## Prosper/PSTricks examples

The next set of examples were prepared for PMA101 using Prosper and PSTricks. Prosper is a LaTeX package that allows you to produce PDF files that work like PowerPoint presentations: you can open them up in Adobe Acrobat, then press the space bar repeatedly to make the steps of a calculation appear in sequence. PSTricks is another LaTeX package that allows you to draw complex diagrams. It works well with Prosper, so you can build up diagrams in steps and make them move around. Here is an example file, containing
• A diagrammatic proof of the relation sin(a+b)=sin(a)cos(b) + cos(a)sin(b)
• An explanation of the chord and the tangent and the definition of a derivative.
• An explanation of the fact that integration calculates the area under a curve.