Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. Very little is known of Euclid's life, and most information comes from the philosophers Proclus and Pappus of Alexandria many centuries later. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, and Theaetetus. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Published in Smarandache Notions Journal, reprinted with permission and this review also appears on Amazon.Euclid ( / ˈ j uː k l ɪ d/ Greek: Εὐκλείδης fl. For this reason you should buy this book and keep a copy on your shelf. Geometry is a jewel that was born on the banks of the Nile river and we should treasure and respect it as the seed from which so much of our basic reasoning sprouted. In so many ways, Euclidean geometry is but the middle way between the other two geometries, a point well made and in great detail by Coxeter. His explanations of the non-Euclidean geometries is so clear that one cannot help but absorb the essentials. While fifty years is a mere spasm compared to the time since Euclid, it is certainly possible that students will be reading Coxeter far into the future with the same appreciation that we have when we read Euclid. The other two, elliptic and hyperbolic, are the main topics of this wonderful book.Ĭoxeter is arguably the best geometer of the twentieth century but there can be no argument that he is the best explainer of geometry of that century. There were in fact three geometries, all of which are of equal validity. Many tried to remove it, but finally the Holmsean dictum of “once you have eliminated the impossible, what is left, no matter how improbable, must be true,” had to be admitted. That annoying fifth postulate seemed so out of place and yet it could not be made to go away. For many centuries, it was nearly an act of faith that all of geometry was Euclidean. Most of the principles of the axiomatic method, the concept of the theorem and many of the techniques used in proofs were born and nurtured in the cradle of geometry. There are other reasons why geometry should occupy a special place in our hearts. The geometry taught in high schools today is with only minor modifications found in the Euclidean classic. It is one of the most read books of all time, arguably the only book without a religious theme still in widespread use over 2000 years after the publication of the first edition. The only book from the ancient history of mathematics that all mathematicians have heard of is the “Elements” by Euclid. It is generally conceded that much of the origins of mathematics is due to the simple necessity of maintaining accurate plots in settlements. We in mathematics owe so much to geometry. Fortunately, like so many things in the world, trends in mathematics are cyclic and one can hope that the geometric cycle is on the rise. It is a commentary on the recent demise of geometry in many curricula that 33 years elapsed between the publication of the fifth and sixth editions. Originally published in 1942, this book has lost none of its power in the last half century.
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