MathDB

A7

Part of 1952 Putnam

Problems(1)

Putnam 1952 A7

Source:

5/29/2022
Directed lines are drawn from the center of a circle, making angles of 0,±1,±2,±3,…0, \pm 1, \pm 2, \pm 3, \ldots (measured in radians from a prime direction). If these lines meet the circle in points P0,P1,P−1,P2,P−2,…,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±i.P_{\pm i}. (You may assume that π\pi is irrational.)
Putnam