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Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..

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Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

Making Tracks

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Perhaps find a bicycle and experiment.

Or perhaps trace a curve on paper and imagine a cyclist following that curve with the front wheel, and then consider the possibilities for the back wheel ?

You may also like to consider the motions recorded in these three images. One line traces the path of a back wheel and one line traces the path of a front wheel: