Mathematics and Euclid

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Euclid also known as Euclid of Alexandria, was a Greek mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy 1 between 323 and 283 BC. Neither the year nor the place of his birth has been established, and the circumstances of his death remain a mystery. Little is known about Euclid other than his writings, the little information known about Euclid comes from commentaries by Proclus and Pappus of Alexandria. Euclid attended the great library of Alexandria and may have studied at Plato's Academy in Greece. Euclid's life span is unknown and he was often confused with Euclid of Megara, who was a Greek Socratic philosopher who live about a century earlier. His elements is the most successful textbook in the history of mathematics. The principles of geometry are deduced from a small set of axioms. Euclid's method of proving mathematical theorems by logical reasoning from accepted first principles continues to be the backbone of mathematics and is responsible for that field's characteristics rigor. Elements is best-known for its geometric results, but it also includes many results in number theory, for example the connection between perfect numbers and Mersenne primes, the proof of the infinitude of prime numbers, Euclid's lemma on factorization this leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations, and the Euclidean algorithm for discovering the greatest common divisor of two numbers. Many of the results in Elements originated with earlier mathematicians so one of Euclid's accomplishments was to present them in a single, logically coherent framework, including a system of rigorous mathematical proofs that remains the basis of mathematics twenty-three centuries later. Euclid's text also includes section on three dimensional geometry and treating plane geometry. The geometrical system presented in the Elements was known simply as geometry and was thought to be the only geometry...
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