In the article Eureka you can find out about Archimedes who was a brilliant early mathematician. Here you can follow these instructions to draw Archimedes' Spiral:
You will need:
4.Starting at the cotton reel end, wind the paper around the reel, again as tightly as you can, right up to the pen.
6.Gradually unravel the strip keeping the pen upright so that it marks the path on the paper. Be careful to control the unwinding! You'll probably need to swap hands as you go along.
If you cut along the outside edge of your spiral (smoothing out any bumps!) and attach a piece of string to the centre, you can hang it above a lamp. Watch what happens to the spiral when you turn the light on. Make sure you leave a gap (at least 20cm) between the end of the spiral and the lamp.