MathDB
Countably many sane points

Source: ICMC 2021 Round 1 P1

March 1, 2022
geometryCountableuncountableICMCcollege contests

Problem Statement

A set of points in the plane is called sane if no three points are collinear and the angle between any three distinct points is a rational number of degrees.
(a) Does there exist a countably infinite sane set P\mathcal{P}?
(b) Does there exist an uncountably infinite sane set Q\mathcal{Q}?
Proposed by Tony Wang