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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?

The Perforated Cube

Stage: 4 Challenge Level: Challenge Level:1
The Freudenthal Institute for Science and Mathematics Education has some very useful Java interactivities.

Follow this link if you would like to explore these environments (but perhaps read the next paragraph first) : http://www.fi.uu.nl/rekenweb/en/

The best interactivity for this problem is called 'Building Houses ', but 'Building free ' and also 'Building Houses with Side Views ' are also excellent resources for problems of this kind.

Warning : Java can take a few seconds to load.

In 'Building free ' you need to type 5 into the size box if you want to match the context of this Perforated Cube problem.

Below is a screen shot of one 'E S H' arrangement. (to get a screen shot press the Print Screen key on the keyboard then paste the image almost anywhere you want it)

This video provides one arrangement for the letters E, S and H. Click the screen to begin.

An ESH cube