MathDB

We are given an angle

0^o < \phi \le 180^o

and a circular disc. An ant begins its journey from an interior point of the disc, travelling in a straight line in a certain direction. When it reaches the edge of the disc, it does the following: it turns clockwise by the angle

\phi

, and if its new direction does not point towards the interior of the disc, it turns by the angle

\phi

again, and repeats this until it faces the interior. Then it continues its journey in this new direction and turns as before every time when it reaches the edge. For what values of

\phi

is it true that for any starting point and initial direction the ant eventually returns to its starting position?

Problem Statement