# Is he rolling forever?

Geometry Level 3

Above are two tangent circles, a bigger one with radius $$R=1$$ and a smaller one with perimeter $$p=2$$. Imagine you can roll the smaller circle counterclockwise around the bigger circle so that they stay tangent. Only whole revolutions are allowed. You now start rolling the small circle.

After how many revolutions will the midpoint of the small circle be back exactly at his red marked starting position as shown above? If you think the small circle will never be back at his starting point answer $$0$$

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