Play the animation or move the slider for \(b\). What do you notice? What questions do you have?

You might like to think about some of the following questions for different values of \(b\). For example, when \(b = 0.38, 0.5, 1\).

- How many regular pentagons can you see?
- What fraction of the shape is shaded in each different colour?
- Can you find the area of any of the shapes?
- Can you see any sequences in the diagram?
- Can you make any links to geometric series? (You may wish to look at Square spirals if you haven’t already done so.)