问题:⊙O的半径为 R,有小圆 A,其半径为 r,小球 A 沿⊙O的内(外)壁滚动一周,回到原来位置时,小圆 A 要自转几圈?这个问题通常称为圆内转圈问题,原为美国一所大学的入学测试题,据说答对者寥寥无几,后传到国内,一时风靡.时至今日,仍常见诸刊物,对对错错,争论颇多.一方面说明这个问题有趣,吸引了许多人的注意,另一方面说明这一问题有一定的难度,因为出错的人多.事实上,广大初中数学教师中对这一问题不能正确解答的人不在少数,有的人即使知道正确结果,也是 Question: The radius of ⊙O is R, there is a small circle A, its radius is r, and the small ball A rolls along the inner (outer) wall of ⊙O once a week. When it returns to its original position, does circle A need to rotate several times? This problem This problem is often referred to as an inner circle circle problem. It was originally an entrance test for a U.S. university. It is said that there are few respondents and it has spread to the country. It is now popular. Today, there are still various publications that are common and there are many disputes. On the one hand, this problem is interesting and attracts many people’s attention. On the other hand, it is difficult to explain this problem because there are many people who make mistakes. In fact, the majority of mathematics teachers in junior middle schools cannot correctly answer this question. Not a few people, even if some people know the correct result, it is