This is a list of topics named after the Greek mathematician

Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Elements'' treatise, which established the foundations of ge ...

Mathematics

Number theory

Euclidean algorithm In mathematics, the Euclidean algorithm,Some widely used textbooks, such as I. N. Herstein's ''Topics in Algebra'' and Serge Lang's ''Algebra'', use the term "Euclidean algorithm" to refer to Euclidean division or Euclid's algorithm, is an effi ...

Extended Euclidean algorithm In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers ''a'' and ''b'', also the coefficients of Bézout's ...

Euclidean division In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than ...

Euclid–Euler theorem The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and only if it has the form , where is a prime number. The theorem is named after mathematician ...

Euclid number In mathematics, Euclid numbers are integers of the form , where ''p'n''# is the ''n''th primorial, i.e. the product of the first ''n'' prime numbers. They are named after the ancient Greek mathematician Euclid, in connection with Euclid's theor ...

Euclid's lemma In algebra and number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely: For example, if , , , then , and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as we ...

Euclid's orchard In mathematics, informally speaking, Euclid's orchard is an array of one-dimensional "trees" of unit height planted at the lattice points in one quadrant of a square lattice. More formally, Euclid's orchard is the set of line segments from to , ...

Euclid–Mullin sequence The Euclid–Mullin sequence is an infinite sequence of distinct prime numbers, in which each element is the least prime factor of one plus the product of all earlier elements. They are named after the ancient Greek mathematician Euclid, because the ...

Euclid's theorem Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proved by Euclid in his work '' Elements''. There are several proofs of the theorem. Euclid's proof Euclid off ...

Algebra

Euclidean domain In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of integers. ...

Euclidean field In mathematics, a Euclidean field is an ordered field for which every non-negative element is a square: that is, in implies that for some in . The constructible numbers form a Euclidean field. It is the smallest Euclidean field, as every Eu ...

Geometry

Euclidean group In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space \mathbb^n; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations) ...

Euclidean geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axiom ...

Non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...

* Euclid's formula *

Euclidean distance In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore o ...

** Euclidean distance matrix *

Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean ...

Pseudo-Euclidean space In mathematics and theoretical physics, a pseudo-Euclidean space is a finite- dimensional real -space together with a non- degenerate quadratic form . Such a quadratic form can, given a suitable choice of basis , be applied to a vector , giving q( ...

Euclidean vector In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors a ...

Euclidean relation In mathematics, Euclidean relations are a class of binary relations that formalize " Axiom 1" in Euclid's ''Elements'': "Magnitudes which are equal to the same are equal to each other." Definition A binary relation ''R'' on a set ''X'' is Euclid ...

Euclidean topology In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on n-dimensional Euclidean space \R^n by the Euclidean metric. Definition The Euclidean norm on \R^n is the non-negative function \, \cdot\, ...

* Euclid's fifth postulate

Other

Euclid's Elements The ''Elements'' ( grc, Στοιχεῖα ''Stoikheîa'') is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postul ...

Euclid's Optics Euclid's ''Optics'' ( grc-gre, Ὀπτικά), is a work on the geometry of vision written by the Greek mathematician Euclid around 300 BC. The earliest surviving manuscript of ''Optics'' is in Greek and dates from the 10th century AD. The wo ...

Euclid (spacecraft) Euclid is a visible to near-infrared space telescope currently under development by the European Space Agency (ESA) and the Euclid Consortium. The objective of the Euclid mission is to better understand dark energy and dark matter by accurately ...

Euclid, Ohio Euclid is a city in Cuyahoga County, Ohio, United States. It is an inner ring suburb of Cleveland. As of the 2020 census, the city had a total population of 49,692. History The City of Euclid was originally a part of Euclid Township, first ma ...

Euclid, Minnesota * Euclidean rhythm a term coined by

Godfried Toussaint Godfried Theodore Patrick Toussaint (1944 – July 2019) was a Canadian computer scientist, a professor of computer science, and the head of the Computer Science Program at New York University Abu Dhabi (NYUAD) in Abu Dhabi, United Arab Emirates. ...

in his 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms" * Euclid (computer program) *

Euclid (programming language) {{Infobox programming language , name = Euclid , logo = , paradigm = multi-paradigm: structured, imperative, functional , year = 1970s , designer = Butler Lampson, Xerox PARC , developer = Ric Holt and James Cordy , latest_release_vers ...

* Euclid, a supercomputer built by the fictional character Maximillian Cohen in the 1998 film π * Euclid Creek * Euclid Avenue, a street in

Manassas, Virginia Manassas (), formerly Manassas Junction, is an independent city in the Commonwealth of Virginia, United States. The population was 42,772 at the 2020 Census. It is the county seat of Prince William County, although the two are separate jurisdi ...

* Euclid Avenue, a street in

Arlington Heights, Illinois Arlington Heights is a municipality in Cook County with a small portion in Lake County in the U.S. state of Illinois. A suburb of Chicago, it lies about northwest of the city's downtown. Per the 2020 Census, the population was 77,676. Per th ...

* Euclid Avenue, a street in

Miami Beach, Florida Miami Beach is a coastal resort city in Miami-Dade County, Florida. It was incorporated on March 26, 1915. The municipality is located on natural and man-made barrier islands between the Atlantic Ocean and Biscayne Bay, the latter of which s ...

* Euclid Avenue, a street in

Des Moines, Iowa Des Moines () is the capital and the most populous city in the U.S. state of Iowa. It is also the county seat of Polk County. A small part of the city extends into Warren County. It was incorporated on September 22, 1851, as Fort Des Moines, ...

* Euclid St, a street in

Orange County, California Orange County is located in the Los Angeles metropolitan area in Southern California. As of the 2020 census, the population was 3,186,989, making it the third-most-populous county in California, the sixth-most-populous in the United States ...

* Euclid, an object designation within the SCP Foundation stories, denoting an anomaly that is difficult, but fairly straightforward to contain. * Mount Euclid in New Zealand's Paparoa Range was named after him in 1970 by the Department of Scientific and Industrial Research. * Euclidate

References

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