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 ?(b) Does there exist an uncountably infinite sane set ?Proposed by Tony Wang