Euclid Essay, Research Paper

Euclid of Alexandria is thought to have lived from about 325 BC until 265 BC in Alexandria, Egypt. There is very little known about his life. It was thought he was born in Megara, which was proven to be incorrect. There is in fact a Euclid of Megara, but he was a philosopher who lived 100 years before Euclid of Alexandria. Also people say that Euclid of Alexandria is the son of Naucrates, but there is no proof of this assumption. Euclid was a very common name at that time, so it was hard to distinguish one Euclid from another. That is the big reason why there is little known about Euclid of Alexandria.

Euclid of Alexandria, whose chief work, Elements, is a comprehensive treatise on mathematics in thirteen volumes on such subjects as plane geometry, proportion in general, the properties of numbers, incommensurable magnitudes, and solid geometry. He was probably educated at Athens by pupils of Plato. He taught geometry in Alexandria and founded a school of mathematics there. The Data, a collection of geometrical theorems; the Phenomena, a description of the heavens; the Optics: the Division of the Scale, a mathematical discussion of music; and several other books have been attributed to him. Historians disagree as to the originality of some of his other contributions. Probably, the geometrical sections of the Elements were primarily a rearrangement of the works of previous mathematicians such as those of Eudoxus, but Euclid himself is thought to have made several original discoveries in the theory of numbers.

Euclid laid down some of the conventions central to modern mathematical proofs. His book The Elements, written about 300 BC, contains many proofs in the field of geometry and algebra. This book illustrates the Greek practice of writing mathematical proofs by first clearly identifying the initial assumptions, and then reasoning from them in a logical way in order to obtain a desired conclusion. As part of such an argument, Euclid used results that had been shown to be true, called theorems, or statements that were explicitly acknowledged to be self-evident, called axioms; this practice continues today.

One of Euclid?s finds is explained in the ninth book of the Elements. It contains proof of the preposition that the number of primes is infinite; that is, no largest number exists. He claims the proof is ?remarkably simple?. Let p be a prime and q=1 x 2 x 3 x? x p+1; That is, one more than the product of all the integers from 1 through p. The integer q is larger than p and is not divisible by any integer from 2 through p, inclusive. Any one of its positive divisors, other than 1, and any one of its prime divisors, therefore, must be larger than p. It follows that there must be a prime larger than p.

Although little is known about Euclid himself, his work is known by many. Even though The Elements is his best known work, he has written a number of works. Each one of his works has provided us with a tremendous amount of valuable information. Today?s modified version of his first few works form the basis of high school instruction in plane geometry.

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