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There are lots of different spirals and lots of different ways of creating them.
One way of making a spiral is by following the instructions to make Archimedes' Spiral.
Another type of spiral is a Golden (or Fibonacci) Spiral.
Can you see how this one has been made?
When you've looked carefully at the picture and thought about this, have a look at the instructions for making a Golden Spiral:
What do you notice about these spirals? Are they similar?
Can you create any more rules for making your own spirals?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?