Problem: A popular brain teaser is to consider the motion of aquarter when you roll it around another one; how many times willWashington’s head rotate while the quarter rolls once around theother fixed quarter. This problem is a generalization of thispuzzle. Assume a system of units such that the radius of thequarter is equal to one unit. Your task is to determine aparameterized position vector describing the location of the whitedot on the rim of the rolling quarter. As the quarter moves, thisdot will sweep out a curve in space. Derive the parametricequations for the curve and plot it. Include a copy or sketch ofyour plot. Hint: The center of the rolling quarter travels along acircle of radius 2
