3550.51 – A Wheel Within A Wheel
A wheel of radius 10" rolls inside a wheel of radius 54". Point on the little wheel starts at point on the big wheel. After how many revolutions of the little wheel do the points and coincide again?
The problem may be re-conceived as follows. Unroll each wheel into a straight line segment. Then the problem asks how many copies of the little line segment are needed to exactly measure a whole number of copies of the big line segment. The ratio of the radii (in lowest terms) is so that copies of the little segment will exactly measure copies of the big line segment. The answer is .