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NRICH: How Far Does it Move?

Experiment with the interactivity of “rolling” regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Take a look at the interactivity below which shows regular polygons “rolling” along the horizontal surface.
It leaves a trace of the path of the dot and on the graph it records the distance that the dot travels.

Experiment by positioning the 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 distance / time graph.

Challenge:

Can you now work out what produced the following distance / time graph?
Can you work out how many sides the polygon hadÂ and where the dot was placed?
Try to explain how you worked it out.

Age 11 to 14

Math Topics
Algebra & Pre-Algebra, Functions & Graphs
Middle School, High School, Educator

## Organization

NRICH (University of Cambridge)

## Type of Resource

Challenge
Online Interactive Activity