OneUnitError
The circle A rolls around the fixed circle B on the outside. The ratio between the radii of A and B is given by the whole number e, either or .
A completes a small cycle when it rotates a full turn about its center, and completes a large cycle when it returns to its starting configuration (a configuration is the set of positions of all points of A).
Question: How many small cycles in a large cycle?
Hint: Check the "Show Markers" checkbox to see the result .
Extensions: When the ratio e is extended to non-integer, the problem becomes more complicated. Let N be the number of small cycles in a large cycle, called "the size of large cycle". Let's derive N from e, fist in case e being rational, then irrational.