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Euclid: The Father of Geometry

Euclid is considered by many to be the father of reason and intellect, advancing mankind from appeals to the gods to the application of the thinking faculties. The truth is that he built on the work of centuries of Greek thinkers including Thales of Miletus and Anaximander. Yet it was Euclid who encapsulated their approach to thinking in such a thorough and foolproof way that its lasting adoption was guaranteed. We don’t know much about the life of Euclid the man. It is believed that he lived around 300 BCE in the great Egyptian city of Alexandria. That city, founded a few decades earlier by Alexander the Great, was home to a huge Museum and Library, the greatest educational institution in the world at that time. Euclid was a teacher of mathematics at Alexandria. It is possible that he was a student of Plato. Several anecdotes have survived to give us glimpses into his character. One source described him as being … most fair and well disposed towards all who were able in any measure to advance mathematics, careful in no way to give offense, and although an exact scholar never vaunting himself. A story is related to how Egyptian ruler King Ptolemy asked Euclid if he had to read the whole of his landmark book on geometry Elements to learn the subject. In response, Euclid is supposed to have said … There is no royal road to geometry. So little is known about the life of the man that it has been suggested that the name Euclid is actually the name that a group of Alexandrian mathematicians gave to themselves when publishing Elements. Still, whether it was written by one man or many, there is no doubt that Elements is one of the most important books ever written. Elements are basically about geometry, the study of shape. It contains all of the basic rules to do with triangles, squares, rectangles, and other shapes that children are taught in school today. But the book did more. It quantified a whole new way to think - one that was based upon logic, deductive reading, evidence, and proof. By using these methods people could uncover the natural rules that governed the workings of the world. Euclid’s great accomplishment was not in the uncovering of new facts about new geometric shapes, but in combining geometrical theorems into a coherent framework of basic theory and proofs. This is the basis of modern science. By turning mathematics into a logical system, Euclid gave it extraordinary power. He introduced the idea of proofs and the idea that rules could be worked out logically from certain assumptions. Assumptions could then be combined to create a theorem. The 5 key axioms in Euclid’s Elements are … Part of a line can be drawn between two given points. 2. Such a part line can be extended indefinitely in either direction. 3. A circle can be drawn with any radius with any given point at its center. 4. All right angles are equal. 5. If part of a line crosses two other lines so that the inner angles on the same sides add up to less than two right angles, then the two lines it crosses must eventually meet. With these watertight definitions, it was possible to establish firm proofs of otherwise vague hunches. The last of Euclid’s axioms - if part of a line crosses two other lines so that the inner angles on the same side add up to exactly two right angles, then the two lines it crosses must be parallel - is called the parallel postulate. It was held a basic central truth but Euclid was not entirely happy with it. He was right to have reservations. Euclidean geometry works perfectly on flat surfaces. Just as the Earth’s surface is not actually flat, however much it appears to be, space is actually curved and has many more than three dimensions, including that of time. Euclid's parallel postulate means that only one line can be drawn parallel to another through a given point, but if space is curved and multidimensional, many other parallel lines can be drawn. Similarly, according to Euclid’s geometry, the internal angles of a triangle always add up to 180 degrees – yet those of a triangle drawn on a ball add up to more than 180. It wasn’t until the 19th century that mathematicians such as Carl Gauss began to realize the limitations of Euclidean geometry and develop new geometric concepts to cover curved space. Yet, the work that Euclid did in the 3rd century BCE has formed the foundation of geometry for more than 2 millennia. Even more profoundly, his insistence on establishing truth by water-tight reasoning based on logic, deduction, evidence, and the proof has been the bedrock of every advancement through history. Credits: Illustration - Jonathan Benbow bongwedesign.com Script - Steve Theunissen Voice Actor - James Fowler Almost in F - Tranquillity by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/... Source: http://incompetech.com/music/royalty-... Artist: http://incompetech.com/