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 ge ...
, an ancient Greek mathematician. It is the name of:
Geometry
*
Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional generalizations
*
Euclidean geometry, the study of the properties of Euclidean spaces
*
Non-Euclidean geometry, 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, the division which produces a quotient and a remainder
*
Euclidean algorithm, a method for finding greatest common divisors
*
Extended Euclidean algorithm, 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
*
Euclidean division of the Intermediate Math League of Eastern Massachusetts
See also
*
Euclid (disambiguation)
*
Euclid's ''Elements'', a 13-book mathematical treatise written by Euclid, that includes both geometry and number theory
*
Euclideon, an Australian computer graphics company
{{disambiguation
Mathematics disambiguation pages