Yet another proof from the Book: the Gauss theorem on regular polygons

摘要

This note is purely expository. The statement of the Gauss theorem on theconstructibility of regular polygons by means of compass and ruler is simpleand well-known. However, its proofs given in most textbooks rely upon muchunmotivated material and are far from being economic. In this note a shortelementary proof of the Gauss theorem is presented. The note is accessible forstudents familiar with polynomials and complex numbers, and could be aninteresting easy reading for professional mathematicians.