Using the standard definition the one revolution is 360 degrees. Look carefully at the rotation of the coin about the other coin. Though it appears that the outer coin rotates twice as it goes around the center coin, it does not. It does one half a revolution from the top to the bottom, then completes another half from the bottom to the top. From the top coin as a reference, the right side of the coin is engaged in the first half of the rotation and the left side in the second half. A third way to see this is the contact point of the top coin is at the bottom of the coin, this point does not come back into contact with the center coin until it reaches the top position. The optical illusion comes from the orientation of the coin when it is at the bottom. Though the orientation is the same as when it is at the top, it is the top of the coin in contact the the center coin not the bottom point. The outer coin only does one 360 rotation as it rolls around the center coin.

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