Euclidean (or, less commonly, Euclidian) is an adjective derived from the name of

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 ...

, an ancient Greek mathematician. It is the name of:

Geometry

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 sp ...

, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional generalizations *

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 axioms ...

, the study of the properties of Euclidean spaces *

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 ...

, systems of points, lines, and planes analogous to Euclidean geometry but without uniquely determined parallel lines *

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 ...

, the distance between pairs of points in Euclidean spaces * Euclidean ball, the set of points within some fixed distance from a center point

Number theory

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 ...

, the division which produces a quotient and a remainder *

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 ...

, a method for finding greatest common divisors *

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 ...

, a method for solving the Diophantine equation ''ax'' + ''by'' = ''d'' where ''d'' is the greatest common divisor of ''a'' and ''b'' *

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 ...

: if a prime number divides a product of two numbers, then it divides at least one of those two numbers * Euclidean domain, 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

* Euclidean relation, a property of binary relations related to transitivity * Euclidean distance map, a digital image in which each pixel value represents the Euclidean distance to an obstacle * Euclidean zoning, a system of land use management modeled after the zoning code of Euclid, Ohio *

of the Intermediate Math League of Eastern Massachusetts

Geometry

Number theory

Other

See also