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...
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