FREE ESSAY ON EUCLID

EUCLID

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.