Euclid

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For other uses of this word, see Euclid (disambiguation).

Euclid

Born	fl. 300 BC
Residence	Alexandria, Egypt
Nationality	Greek
Field	Mathematics
Known for	Euclid's Elements

Euclid (Greek: Εὐκλείδης -- Euklidis), also known as Euclid of Alexandria, "The Father of Geometry" was a Greek mathematician of the Hellenistic period who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323 BC-283 BC). His Elements is the most successful textbook in the history of mathematics. In it, the principles of Euclidean geometry are deduced from a small set of axioms. Furthermore, Euclid's method of proving mathematical theorems by logical reasoning from accepted first principles remains the backbone of mathematics and is responsible for that field's characteristic rigor (see Mathematics). Although best-known for its geometric results, the Elements also includes various results in number theory, such as the connection between perfect numbers and Mersenne primes, the proof of the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.

Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces.

Contents 1 Other works 2 Biographical sources 3 Tributes 4 See also 5 References 6 External links

[edit] Other works

In addition to the Elements, five works of Euclid have survived to the present day.

• Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
• On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century (AD) work by Heron of Alexandria
• Optics, the earliest surviving Greek treatise on perspective, contains propositions on the apparent sizes and shapes of objects viewed from different distances and angles.
• Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors.

All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions.

There are four works credibly attributed to Euclid which have been lost.

• Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject.
• Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial.
• Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning.
• Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces.

[edit] Biographical sources

Little is known about Euclid other than his writings. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria: Euclid was active at the great Library of Alexandria and may have studied at Plato's Academy in Greece. Euclid's exact lifespan and place of birth are unknown. Some writers in the Middle Ages confused him with Euclid of Megara, a Greek Socratic philosopher who lived approximately one century earlier.

[edit] Tributes

Astronomical

• 4354 Euclides is an asteroid named after Euclid
• Euclides (7.4S, 29.5W, 12km dia, 1.3 km depth) is a lunar crater named after him

Place names

• Many cities and towns have a street called "Euclid Street" or "Euclid Avenue"; the most well-known is Euclid Avenue in Cleveland, Ohio.
• In Benton Harbor, Michigan, Euclid Avenue runs parallel to Napier Avenue, a street that shares its name with the 17th century mathematician John Napier.
• The city of Euclid, Ohio, population 52,000+, a suburb of Cleveland, Ohio.
• In Littleton, Colorado there is a Euclid Middle school located on Euclid Avenue

Poetry

• "Euclid Alone Has Looked on Beauty Bare", a poem written by Edna St. Vincent Millay in 1923

Other

• The Euclid math competition, from the University of Waterloo.

Popular culture

• Euclid was ranked #14 in Michael H. Hart's book, The 100: A Ranking of The Most Influential Persons in History.
• "Euclid" is the name of a town in the SNES game, Tales of Phantasia
• "Euclid" was the computer's name in the movie Pi