Euclid and the Infinitude of Primes Summary and Analysis

In the third chapter, Dunham looks at the remainder of Euclid's Elements in summary. Euclid goes on to prove other relationships within geometric figures and demonstrates how to construct regular polygons such as a hexagon, a pentagon and a pentadecagon of 15 sides.

Dunham then turns to Euclid's number theory, which examines the nature of whole numbers. While it may seem too basic compared to the more complex theorems of geometry, Dunham warns that number theory is actually very important even in modern math.

Euclid defines even and odd numbers and then moves on to define prime numbers, those special numbers which can only be divided by 1 and themselves. Numbers which can be divided by numbers other than one and themselves he calls composite numbers. Euclid defines the concept of perfect numbers...