By Tompson Hsu His LifeEuclid: Father of Geometry, Greek scholar, thinker, and one of the most influential figures in the field of mathematics. Yet, even with such an impressive track record, much of his actual identity and life remains shrouded in mystery. For starters, the person that most people commonly refer to as Euclid can be known more specifically as “Euclid of Alexandria”, named so after his place of residence, in order to distinguish him from other Euclids from the time. From the few original documents that have been preserved, it is estimated that his time of birth was most likely around 325 BC. On the other hand, there exist Arabian documents which go into much more detail, such as a birth town in Tyre, although these are not regarded as reliable by historians. Another uncertainty is the notion that the alias “Euclid” was actually a pseudonym used by a group of mathematicians, as opposed to a single person—once again, though, historians do not give much credit to this idea. However, unlike the details of his life, his work, including Elements and some other lesser-known ones, continue to be highly prestigious textbooks for the study of mathematics long after his death in 270 BC. His WorkTo discuss the contributions of Euclid without bringing up first and foremost his magnum opus, Elements, would be nothing short of a cardinal disrespect to such a well-revered document. Indeed, up until the 19th and 20th centuries—more than 2000 years later after its publication—this text remained the primary textbook for the education of mathematics and geometry. Elements is the name given to describe Euclid’s collection of 13 books, written and assembled in 300 BC, chock full of definitions, theorems, proofs, and postulates. Although many of the ideas expressed in these works were, admittedly, not entirely original, Euclid’s Elements served as the first and only collection of these mathematical topics into a single, comprehensive work. The books not only helped solidify knowledge about geometry as a genuine field of mathematics via the use of rigorous proofs (a practice he helped popularize) but also worked to bring together ideas from a wide variety of topics, from the Pythagorean theorem and conics, to prime numbers, square roots, and irrationality. And yet, the most striking contents resided in the very first book of Elements, which contained Euclid’s 5 axioms and 5 common notions. The common notions were named as such due to their simplistic nature—for example, the 5th declares that a whole is greater than a part. However, Euclid’s axioms pose much more revolutionary materials—more specifically, the 5th one, the parallel postulate, controversial in its nature due to its error. The parallel postulate claimed that in two dimensional geometry, “If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.” Euclid, at the time of writing, may have understood fully the controversy of including this axiom in his work, because he himself failed to prove it. However, in order to maintain all the other parts of his geometry, it was necessary to be included-leading to the later categorization of Euclidean geometry, and the geometries which did not obey the 5th axiom, appropriately named “Non-Euclidean geometry”. Nevertheless, even with minor modern contradictions, the rest of his writings still hold strong thousands of years later, as one of the most reproduced works of writing in the history of mankind, second only to the Holy Bible. Euclid’s Elements, and the great wealth of knowledge it imprinted upon the world in so many more ways than just those above, were undeniably without equal in their influence on math. As a Greek thinker and scholar, however, Euclid was not limited to only mathematics, nor was he limited to just the Elements. He wrote extensively, and on a great multitude of topics. Unfortunately, many of these works (Conics, Porisms, Pseudaria, Surface Loci, On the Balance, etc.) were destroyed or lost over time, and very little is known about them. Of the works that remain, however, much can also be gleaned. For example, Euclid’s Phaenomena, a treatise on spherical astronomy, as well as his Data (regarding implications of “given” informations in problems) are very closely tied with his Elements—as was his On the Divisions of Figures, (survived only in an Arabic translation) a work about ratios. Contrasting the mathematical nature of those works were Optics and Catoptrics, which dealt with the matters perspective and mirrors, respectively. CONCLUSIONAlthough Euclid’s life and identity will remain unsolved mysteries, his works have existed as great boons to modern education and our understanding of not only geometry, but of mathematics as a field. While Euclid may not have been the most influential figure, his contributions have certainly played a significant part in the whole of mankind’s history. CITATIONS“Euclid's Elements.” Wikipedia, Wikimedia Foundation, 17 Feb. 2018, en.wikipedia.org/wiki/Euclid%27s_Elements YourDictionary. “Who Is Euclid and What Did He Do?” YourDictionary, 12 July 2013, biography.yourdictionary.com/articles/who-is-euclid-and-what-did-he-do.html Waerden, Bartel Leendert van der, and Christian Marinus Taisbak. “Euclid.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 2 Feb. 2018, www.britannica.com/biography/Euclid-Greek-mathematician. Weisstein, Eric W. “Elements.” From Wolfram MathWorld, mathworld.wolfram.com/Elements.html Suggested ReadingsSzabó, Árpád (1978). The Beginnings of Greek Mathematics. A.M. Ungar, trans. Dordrecht, Holland: D. Reidel.
Mueller, Ian (1981). Philosophy of Mathematics and Deductive Structure in Euclid's Elements.
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