Making Maths: Archimedes' Spiral

Stage: 2 and 3 Challenge Level: Challenge Level:1

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:

  • Cotton reel
  • Pencil or pen
  • Scissors
  • Paper - one sheet approx A4 size and one much larger (at least A3)
  • Sticky tape
  • Ruler
  • Someone to help you!
1.Cut a strip of paper from the A4 sheet at least 25cm long and the same width as the cotton reel (don't include the ridges at each end of the cotton reel when you work out its width).
2.Tape one end of the strip to the cotton reel, making sure that the edge of the paper is parallel to (in line with) the edge of the reel and that the strip fits inside the ridges of the cotton reel.
3.Lay out the cotton reel with the paper going underneath it. Place the pen or pencil at the other end of the strip. Fold a bit of the paper quite tightly over the pen and tape it down.

4.Starting at the cotton reel end, wind the paper around the reel, again as tightly as you can, right up to the pen.

5.Ask your friend to hold the cotton reel steady in the middle of the large sheet of paper.

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.

There you have it - an Archimedean Spiral.

Try this:

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.

This activity featured in our December 2008 Advent Calendar .