| Euclid | |
 |
|
| Born | fl. 300 BC |
|---|---|
| Residence | Alexandria, Egypt |
| Nationality | Greek |
| Fields | Mathematics |
| Known for | Euclid's Elements |
Euclid (Greek: Εὐκλείδης — Eukleidēs), fl. 300 BC, also known as Euclid of Alexandria and the "Father of Geometry", was a Greek mathematician of the Hellenistic period who was active in Alexandria, almost certainly during the reign of Ptolemy I (323 BC–283 BC). Alexandria ( Egyptian Arabic: اسكندريه Eskendereyya; Standard Arabic: ar الإسكندرية Al-Iskandariyya; Ἀλεξάνδρεια This article is about the country of Egypt For a topic outline on this subject see List of basic Egypt topics. Greece (Ελλάδα transliterated: Elláda, historically, Ellás,) officially the Hellenic Republic (Ελληνική Δημοκρατία Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Euclid's Elements ( Greek:) is a mathematical and geometric Treatise consisting of 13 books written by the Greek Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly Events By place Egypt Pyrrhus, the King of Epirus, is taken as a hostage to Egypt after the Battle of Ipsus Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position Greek mathematics, as that term is used in this article is the Mathematics written in Greek, developed from the 6th century BC to the 5th century This article focuses on the cultural aspects of the Hellenistic age for the historical aspects see Hellenistic period. Alexandria ( Egyptian Arabic: اسكندريه Eskendereyya; Standard Arabic: ar الإسكندرية Al-Iskandariyya; Ἀλεξάνδρεια For the astronomer see Ptolemy; for others named "Ptolemy" or "Ptolemaeus" see Ptolemy (disambiguation. Events By place Macedonian Empire 10 June — In Babylon, Alexander the Great dies ten days after being taken ill Events By place Greece Following Demetrius Poliorcetes ' death in captivity as a prisoner of Seleucus, his son Antigonus His Elements is the most successful textbook in the history of mathematics. Euclid's Elements ( Greek:) is a mathematical and geometric Treatise consisting of 13 books written by the Greek A textbook is a manual of instruction or a standard book in any branch of study The area of study known as the history of mathematics is primarily an investigation into the origin of new discoveries in Mathematics and to a lesser extent an investigation In it, the principles of what is now called Euclidean geometry are deduced from a small set of axioms. Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria. In traditional Logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject Euclid also wrote works on perspective, conic sections, spherical geometry, and rigor. Perspective, in context of vision and Visual perception, is the way in which objects appear to the Eye based on their spatial attributes or In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface Spherical geometry is the Geometry of the two- Dimensional surface of a Sphere. Rigour or rigor (see spelling differences) has a number of meanings in relation to intellectual life and discourse
Contents |
Biographical knowledge
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. Proclus Lycaeus ( February 8, c 411 &ndash April 17, 485) called "The Successor" or "Diadochos" ( Greek Próklos Pappus of Alexandria ( Greek) (c 290 &ndash c 350 was one of the last great Greek mathematicians of antiquity known for his Synagoge or Collection The Royal Library of Alexandria or Ancient Library of Alexandria in Alexandria, Egypt, was once the largest library in the ancient world Biography Early life Birth and family Plato was born in Athens Greece An academy ( Greek Ἀκαδημία is an institution of higher learning research or honorary membership Greece (Ελλάδα transliterated: Elláda, historically, Ellás,) officially the Hellenic Republic (Ελληνική Δημοκρατία The date and place of Euclid's birth and the date and circumstances of his death are unknown.
Some writers in the Middle Ages confused him with Euclid of Megara, a Greek Socratic philosopher who lived approximately one century earlier. Euclid of Megara, a Greek Socratic Philosopher who lived around 400 BC founded the Megarian school of philosophy. SOCRATES is the European Community action programme in the field of Education. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language
The Elements
Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.
Although best-known for its geometric results, the Elements also includes number theory. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes It considers the connection between perfect numbers and Mersenne primes, 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. In mathematics a perfect number is defined as a positive integer which is the sum of its proper positive Divisors that is the sum of the positive divisors excluding In Mathematics, a Mersenne number is a positive integer that is one less than a Power of two: M_n=2^n-1 In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 Euclid's lemma ( Greek) is a generalization of Proposition 30 of Book VII of Euclid's Elements. In Number theory, the fundamental theorem of arithmetic (or unique-prime-factorization theorem) states that every Natural number greater than 1 can be written In Number theory, the Euclidean algorithm (also called Euclid's algorithm) is an Algorithm to determine the Greatest common divisor (GCD In Mathematics, the greatest common divisor (gcd, sometimes known as the greatest common factor (gcf or highest common factor (hcf, of two non-zero
The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called Non-Euclidean geometries that mathematicians discovered in the 19th century. Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria. In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar
Other works
In addition to the Elements, at least 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. Data ( Greek: Δεδομένα Dedomena) is a work by Euclid.
- 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. Arabic (ar الْعَرَبيّة (informally ar عَرَبيْ) in terms of the number of speakers is the largest living member of the Semitic language A ratio is an expression which compares quantities relative to each other It is similar to a third century AD work by Heron of Alexandria. The 3rd century is the period from 201 to 300 in accordance with the Julian calendar in the Christian / Common Era. Hero (or Heron) of Alexandria ( Ήρων ο Αλεξανδρεύς) (c
- Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. Catoptrics deals with the phenomena of reflected light and image-forming optical systems using Mirrors From the Greek κατοπτρικός (specular The attribution to Euclid is doubtful. Its author may have been Theon of Alexandria. Theon ( Greek: Θέων ca 335 - ca 405 AD was a Greek (or as some scholars contend an Egyptian) Scholar and Mathematician who lived
- Phaenomena is a treatise on spherical Astronomy, it survives in Greek and is quite similar to "On the Moving Sphere", by Autolycus of Pitane, who flourished around 310 BC. Autolycus of Pitane (c 360 BC–c 290 BC was a Greek Astronomer, Mathematician, and Geographer.
- Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: "Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal. " In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy. Pappus of Alexandria ( Greek) (c 290 &ndash c 350 was one of the last great Greek mathematicians of antiquity known for his Synagoge or Collection Claudius Ptolemaeus ( Greek: Klaúdios Ptolemaîos; after 83 &ndash ca
All of these works follow the basic logical structure of the Elements, containing definitions and proved propositions.
There are also 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. In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface It is likely that the first four books of Apollonius's work come directly from Euclid. According to Pappus, "Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics. " The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid's work was already lost.
- Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial. The subject of porisms is perplexed by the multitude of different views which have been held by Geometers as to what a porism really was and is
- Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning. Reasoning is the cognitive process of looking for Reasons for beliefs conclusions actions or feelings
- 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. In Mathematics, a locus ( Latin for "place" plural loci) is a collection of points which share a property In mathematics a quadric, or quadric surface, is any D -dimensional Hypersurface defined as the locus of zeros of a Quadratic
- Several works on mechanics are attributed to Euclid by Arabic sources. Mechanics ( Greek) is the branch of Physics concerned with the behaviour of physical bodies when subjected to Forces or displacements On the Heavy and the Light contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. On the Balance treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on mechanics written by Euclid.
See also
References
- "Euclid (Greek mathematician)". In Mathematics, an axiomatic system is any set of Axioms from which some or all axioms can be used in conjunction to logically derive Theorems In Number theory, the Euclidean algorithm (also called Euclid's algorithm) is an Algorithm to determine the Greatest common divisor (GCD Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria. Encyclopædia Britannica Online. (2008). Chicago: Encyclopædia Britannica, Inc. Retrieved on 2008-04-18. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 1025 - Bolesław Chrobry is crowned in Gniezno, becoming the first King of Poland.
- Artmann, Benno (1999). Euclid: The Creation of Mathematics. New York: Springer. ISBN 0-387-98423-2.
- Ball, W.W. Rouse (1960). Walter William Rouse Ball ( 14 August 1850 – 4 April 1925) was a British Mathematician, Lawyer and a fellow A Short Account of the History of Mathematics, 4th ed. [Reprint. Original publication: London: Macmillan & Co. , 1908], New York: Dover Publications, 50–62. ISBN 0-486-20630-0. “Of his life we know next to nothing, save that he was of Greek descent . . . ”[p. 52].
- Boyer, Carl B. (1991). Carl Benjamin Boyer ( November 3, 1906 – April 26, 1976) has been called the " Gibbon of math history"he A History of Mathematics, 2d ed. , John Wiley & Sons, Inc. . ISBN 0-47154397-7.
- Heath, Thomas L. (1956). Sir Thomas Little Heath ( October 5, 1861 &ndash March 16, 1940) was a British civil servant Mathematician, classical 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). Morris Kline ( May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy 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. The MacTutor History of Mathematics archive is an award-winning website maintained by John J
External links
- A short list of Mathematicians born in Egypt
- 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). Clark University is a private University and Liberal arts college in Worcester Massachusetts. University of Texas.
- Euclid's elements, All thirteen books, in Spanish and Catalan.
- Elementa Geometriae 1482, Venice. From Rare Book Room. Rare Book Room is an educational website for the repository of digitally scanned rare books made freely available to the public
- Elementa 888 AD, Byzantine. From Rare Book Room. Rare Book Room is an educational website for the repository of digitally scanned rare books made freely available to the public
- 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.
| Persondata | |
|---|---|
| NAME | Euclid |
| ALTERNATIVE NAMES | Euclid of Alexandria; Εὐκλείδης (Greek) |
| SHORT DESCRIPTION | Greek mathematician |
| DATE OF BIRTH | 325 BCE |
| PLACE OF BIRTH | |
| DATE OF DEATH | 265 BCE |
| PLACE OF DEATH | |
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