有这样一道数学题:一枚硬币绕另一个相同的硬币转动一周(不发生滑动),这枚硬币自转了几周?关于圆的滚动的周数的问题,已有多篇论文见诸于国内中学数学杂志,并且也给出了一般性结论:当一个半径为r的圆绕一个半径为R的圆无滑动滚动一周,若两圆外切,则半径为r的圆自转R-rr周;若两圆内切,则半径为r的圆自转R-rr周。然纵观各种证明,基本都是这样的一条路线,即先研究圆沿直线滚动,然后研 There is a mathematical problem: a coin around another coin the same rotation (without sliding), the coin rotation for a few weeks? Circular on the rolling number of weeks, there have been many papers published in the country High school mathematics magazine, and also gives the general conclusion: when a circle with radius r rounds a circle with a radius R rolling without slip for one week, if the two circles are circumscribed, the circle with radius r rotates R-rr weeks; If the two circles are inscribed, then the circle of radius r rotates R-rr weeks. However, looking at all kinds of proof, the basic is such a line, that is to study the circle along a straight line, and then research