Computer graphics for teaching
This web page contains material for a presentation on some uses of
computer-generated graphics in teaching mathematics.
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.
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
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
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.
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
control the animations (so that they can be run forwards or
backwards, slowed down, set to repeat indefinitely, and so on).
The next set of examples were prepared for PMA101 using
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.