Rolling Inside

Weekly Problem 11 - 2007
A circle of radius 1 rolls without slipping round the inside of a square of side length 4. Find an expression for the number of revolutions the circle makes.
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Problem



A circle of radius 1 rolls without slipping round the inside of a square of side length 4. Find an expression involving $\pi$ for the exact number of revolutions the circle makes by the time it returns to its original position.

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Rolling Inside

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.