Euclidean (or, less commonly, Euclidian) is an adjective derived from the name of
Euclid, an ancient Greek mathematician. It is the name of:
Geometry
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Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional generalizations
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Euclidean geometry, the study of the properties of Euclidean spaces
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Non-Euclidean geometry, systems of points, lines, and planes analogous to Euclidean geometry but without uniquely determined parallel lines
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Euclidean distance, the distance between pairs of points in Euclidean spaces
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Euclidean ball
A ball is a round object (usually spherical, but can sometimes be ovoid) with several uses. It is used in ball games, where the play of the game follows the state of the ball as it is hit, kicked or thrown by players. Balls can also be used f ...
, the set of points within some fixed distance from a center point
Number theory
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Euclidean division, the division which produces a quotient and a remainder
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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 ...
, a method for finding greatest common divisors
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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 ide ...
, a method for solving the Diophantine equation ''ax'' + ''by'' = ''d'' where ''d'' is the greatest common divisor of ''a'' and ''b''
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Euclid's lemma: if a prime number divides a product of two numbers, then it divides at least one of those two numbers
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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. ...
, a ring in which Euclidean division may be defined, which allows Euclid's lemma to be true and the Euclidean algorithm and the extended Euclidean algorithm to work
Other
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Euclidean relation, a property of binary relations related to transitivity
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Euclidean distance map
A distance transform, also known as distance map or distance field, is a derived representation of a digital image. The choice of the term depends on the point of view on the object in question: whether the initial image is transformed into another ...
, a digital image in which each pixel value represents the Euclidean distance to an obstacle
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Euclidean zoning
Zoning in the United States includes various land use laws falling under the police power rights of state governments and local governments to exercise authority over privately owned real property. Zoning laws in major cities originated with the ...
, a system of land use management modeled after the zoning code of Euclid, Ohio
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Euclidean division of the Intermediate Math League of Eastern Massachusetts
See also
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Euclid (disambiguation) Euclid, Euclides, or Eucleides generally refers to the ancient Greek mathematician Euclid of Alexandria (3rd century BC), who wrote a work on geometry called the ''Elements''.
It may also refer to:
People
* Euclid of Megara (c. 435 BC–c. 365 BC ...
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Euclid's ''Elements'', a 13-book mathematical treatise written by Euclid, that includes both geometry and number theory
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Euclideon
Euclideon Pty Ltd is an Australian computer software company best known for a middleware 3D graphics engine, called Unlimited Detail. Euclideon is also the parent company and operator of Holoverse, a 'holographic entertainment centre' located ...
, an Australian computer graphics company
{{disambiguation
Mathematics disambiguation pages