EUCLID

:''For other uses of this word, see Euclid (disambiguation).''
'Euclid' (Greek: ''), 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).He was born in Greece. 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

Other works

Biographical sources

Tributes

See also

References

External links

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.

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.

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''

★ "Euclid is the UK Cultural Contact Point in Britain, which produces the popular website www.culture.info

See also

★ Euclidean geometry

References

★ Artmann, Benno (1999). ''Euclid: The Creation of Mathematics''. New York: Springer. ISBN 0-387-98423-2.

★ Bulmer-Thomas, Ivor (1971). "Euclid". ''Dictionary of Scientific Biography.''

★ Heath, Thomas L. (1956). ''The Thirteen Books of Euclid's Elements'', Vol. 1 (2nd ed.). New York: Dover Publications. ISBN 0-486-60088-2: includes extensive commentaries on Euclid and his work in the context of the history of mathematics that preceded him.

★ Heath, Thomas L. (1981). ''A History of Greek Mathematics'', 2 Vols. New York: Dover Publications. ISBN 0-486-24073-8 / ISBN 0-486-24074-6.

★ Kline, Morris (1980). ''Mathematics: The Loss of Certainty''. Oxford: Oxford University Press. ISBN 0-19-502754-X.

★

External links

★ Euclid's elements, All thirteen books, with interactive diagrams using Java. Clark University

★ Euclid's elements, with the original Greek and an English translation on facing pages (includes PDF version for printing) (only the first ten books). University of Texas.

★ in ancient Greek (typeset in PDF format, public domain, available in print at Lulu.com as "Euclid's Elements".)

★ Euclid's elements, All thirteen books, in Spanish and Catalan.

★ ''Elementa Geometriae'' 1482, Venice. From Rare Book Room.

★ ''Elementa'' 888 AD, Byzantine. From Rare Book Room.

★ Euclid biography by Charlene Douglass With extensive bibliography.

★ Euclid's Elements. Heiberg's edition of the Greek with Latin translation (public domain). PDF scans of all 13 books.