The Geometry of Numbers

Abstract

It may seem odd that the first chapter of a book on geometry should be about numbers. But, as was mentioned in the introduction, this book will take the original meaning of geo-metry as world-measurement. So if we consider geometry primarily as a language of measurement then we will need to study the basic tools of measurement, real numbers. Everyone who reads this chapter will know or think they know what real numbers are. However this doesn’t make the chapter superfluous. We will look at real numbers from a geometric viewpoint. The operations of real numbers such as addition and multiplication are all based on geometric considerations. We have all heard of square numbers but there are triangular numbers and pentagonal numbers too.

Counting is what allowed people to take the measure of their world, to understand it better and to put some of its innumerable secrets to good use. Georges Ifrah