# 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**

##
PostScript

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.

## Geometry

**
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
**