Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 28 - 1909  

Research Article

Gauss's Theorem on the Regular Polygons which can be constructed by Euclid's Method

Professor H.S. Carslaw

The methods now adopted in the teaching of elementary geometry have made it most important that the teacher should have clear views upon the nature of the problems which are soluble by Euclid's methods: that is, with the aid of the ruler and compass only. With this general question I have dealt in another place. In this paper I give a short account of the argument by means of which Gauss proved that the only regular polygons of n sides, which can be constructed by Euclid's methods, are those in which n, when broken up into prime factors, takes the form

S0013091500034866_eqnU1

m1, m2, m3,…mr being all different.

(Received October 1909)

(Revised April 25 1909)