What in the world is Euclidean geometry and non-Euclidean Geometry? To answer this question, we first need to understand who Euclid was and what contributions he made to the world of mathematics. Unfortunately, to this day, Euclid’s life is a bit of a mystery, and the only reason anyone knows much about him is because of the Greek philosopher Proclus. From Proclus, we really only know for sure Euclid was a famous Greek mathematician who taught at Alexandria in Egypt. Besides this, we do not know much else about Euclid’s life. We do not know when exactly he was born or when he died. We do not know where he officially died, or if he had a wife or children.

Fortunately, what we do know is that Euclid wrote thirteen books called The Elements, which includes Euclid’s theorems and proofs of geometry and number theory written roughly 2300 years ago, or about 300 BC. The Elements are said to be so important that the only other book which has been so widely translated and circulated is the bible (Drakos). Pretty cool, right? Some of the greatest mathematicians this world has ever know have also studied this book because of how valuable the information in it is.

It is important to note that although Euclid receives all the credit for these books, he was not the only one to contribute to the information in them. Euclid decided one day he wanted to compile information from all the men who came before him, Hippocrates of Chios (about 440 BC) and Theudius, and put all of it into these books. Although, “it is clear that the whole design of his work was his own” (Taisbak et al.) meaning the men who came before him did not help him put all the information together.

When proving the theorems or propositions throughout these books, Euclid made it easy by having all of the information you need within the books. This means you do not need to spend hours searching for new outside information to prove the theorems.