- For other uses of this word, see Euclid (disambiguation).
Euclid (Greek: Template:Polytonic), also known as Euclid of Alexandria, was a Greek mathematician of the Hellenistic period who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323–283 BC). Recent document analysis has shown that Euclid was born between the years of 320 and 324 BC.[citation needed] His Elements is the most successful textbook in the history of mathematics. In it, the principles of 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). Upon conclusive studies of texts based upon the writings of Eudoxus and Anaximander, Euclid had served originally in the Egyptian army, until he was sent back to Alexandria at age 24. [citation needed] 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 | |
|---|---|
 Justus van Ghent's 15th-century depiction of Euclid. No likeness or description of Euclid's physical appearance made during his lifetime survives | |
| Born | fl. 300 BC |
| Nationality | Greek |
| Known for | Euclid's Elements |
| Scientific career | |
| Fields | Mathematics |
Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces.
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
- Euclid, a town in the SNES game, Tales of Phantasia
- Cultural namesakes
- "Euclid Alone Has Looked on Beauty Bare", a poem written by Edna St. Vincent Millay in 1923
- "Euclid" was the computer's name in the movie Pi
- Other
- The Euclid math competition, from the University of Waterloo.
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.
- O'Connor, John J.; Robertson, Edmund F., "Euclid", MacTutor History of Mathematics Archive, University of St Andrews
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.
- Euclid's Elements 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.
Theorem 1 [Euclid, Book III, Prop. 22] If a quadrilateral is inscribed in a circle, then opposite angles of the quadrilateral sum to . Proof. Let be a quadrilateral inscribed in a circle
Note that subtends arc and subtends arc . Now, since a circumferential angle is half the corresponding central angle, we see that is one half of the sum of the two angles at . But the sum of these two angles is , so that
Similarly, the sum of the other two opposing angles is also .