Problem 5 (Rolling Circles)

An interesting, but not so easy problem, is to determine the number of turns a circle will make when rolled around the outside of a fixed circle. For example, suppose you place two pennies, side by side, face up. Now hold one penny and rotate the other around it in the counterclockwise direction. It is not easy to visualize the number of turns the rolling penny makes as it rotates around the outside of the fixed penny. We have two questions, one you can do by physical experimentation, the other with your mind.

• How many turns does the rolling penny make around the outside of the fixed penny ?

• What if the diameter of the rolling circle is 1 and the diameter of the fixed circle is F. How many turns will the rolling circle make around the outside of the fixed circle ?

[Previous]	Problem 4 (Case of the Two Quadratics)
[Next]	Problem 6 (Arithmetic Circles)
[Up]	February Problems
[Home]	Home Page
[Mail]	Send EMail to Maine Math Talent Search
[Contents]	Maine Math Talent Search Contents

Last modified on Monday, February 08, 1999