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?
Find a bicycle and experiment.
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 ?
Above all this is a good
problem not to rush .
Leave the way into this problem left
open and allow students to bring along fresh thoughts
from time to time. The emerging solution will be much more
satisfying and the process a much better experience of real new