Mathematics 308 - Spring 1996 - Euclidean geometry

Spring term

Section 201

2:30-3:30 M W F

Buchanan B216 (a change from what the Registration guide says)

In this course, I will show how mathematics and computers can be used together to produce graphics of mathematical interest. The programming language to be used is PostScript. It is ideal for my purposes because its imaging model uses affine geometry in a crucial manner. Towards the end of the course, elementary 3D graphics including perspective, and perhaps something of the regular solids, will be discussed. Also, at the end of the course students will have to propose and carry out their own projects in mathematical drawing. Students will be given accounts in the Mathematics Department undergraduate computer laboratory, and will also be able to run PostScript on PC-compatible machines or Macintoshes elsewhere.

Course outline

First homework

The format of the homework to be handed in

My version of the programs in the first homework

Second homework

Third homework

Mid-term solutions


These are written especially for this course:

PostScript command summary

Introduction to PostScript

Sample program

A very simple PostScript program

Remarks on GhostScript

Subroutines in PostScript

Loops in PostScript

The drawing environment in PostScript

The following comes from the Net. It seems to be thorough:

A first guide to PostScript

Also check out the nice job David Maxwell has done in our own help facility. Look there for the PostScript reference.


Pythagoras' Theorem

Another proof of Pythagoras' Theorem

Bezier curves

Exponentials of matrices

PostScript routines to find eigenvalues etc. of 2 x 2 matrices (including matrix exponentials)

Drawing parametrized paths with PostScript

The package to draw parametrized paths in 2D

Solutions to the second homework

Introduction to geometry in 3D

How to use the matrix package

The package itself

How to draw polygons and parametrized paths in 3D

The package to help you do this

The term projects