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
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..
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
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
This video provides one
arrangement for the letters E, S and H. Click the screen to