Clock Math
The GeoGebra below shows a clock with N positions. Starting from the N o'clock, the system will draw lines each time jumping J hours ahead.
1. Consider N = 12.
(a) What is the shape of the figure obtained when
(i) J = 3?
(ii) J = 4?
(iii) J = 6?
(b) Which value(s) of J will result in a complete cycle?
[Hint: A complete cycle means the figure visits all the positions.]
(c) Which property must J have to result in a complete cycle?
2. Try other values of N and J. See if your answer in question 1(c) is true.