Rolling a Small Circle
around a
Larger Circle

Given a circle of radius    r     rolling around the outside of larger circle of radius   R   where R = 4r.

How many revolution with the small circle make in rolling around the large circle one time?

Give a mathematical explanation of your answer.

Click HERE for a GSP file to simulate the rolling movement.

Generalize.  What if   R = nr?    How many revolutions of the small circle?

How many revolutions of the small circle if it rolls around the INSIDE of the large circle?

Build a GSP sketch to illustrate rolling a small circle around the inside of a larger circle.


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