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## 'Up and Across' printed from http://nrich.maths.org/

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.

Full
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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.