MathDB

Directed lines are drawn from the center of a circle, making angles of

0, \pm 1, \pm 2, \pm 3, \ldots

(measured in radians from a prime direction). If these lines meet the circle in points

P_0, P_1, P_{-1}, P_2, P_{-2}, \ldots,

show that there is no interval on the circumference of the circle which does not contain some

P_{\pm i}.

(You may assume that

\pi

is irrational.)

Problem Statement