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Take a look at the interactivity below which shows regular polygons "rolling" along the horizontal surface, leaving a trace of the path of the red dot.

A blue dot tracks the height of the red dot whilst a green dot tracks the horizontal distance travelled by the red dot.

The graph records either the horizontal distance travelled by the red dot or the height of the red dot over time.

Experiment by positioning the red dot at the centre of the polygons, at one of the vertices or at the centre of one of the sides of the polygons and explore how this affects the two graphs.

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Challenge:

Can you now work out what produced the following two graphs?
The rolling polygon had a radius of 45.
Can you work out how many sides it had and where the red dot was placed?
Try to explain how you worked it out.

Horizontal distance/time graph
Height/time graph