Editing Euclidean

{{wiktionary|Euclidean|Euclideanness}}
'''Euclidean''' (or, less commonly, '''Euclidian''') is an adjective derived from the name of [[Euclid]], an ancient Greek mathematician.

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== 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]], 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]]: 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 rhythm]], a method of distributing beats across musical steps based on Euclid's algorithm
*[[Euclidean zoning]], a system of land use management modeled after the zoning code of Euclid, Ohio
*[[Intermediate Math League of Eastern Massachusetts#Divisions|Euclidean division]] of the Intermediate Math League of Eastern Massachusetts

== See also ==
*[[Euclid (disambiguation)]]
*[[Euclid's Elements|Euclid's ''Elements'']], a 13-book mathematical treatise written by Euclid, that includes both geometry and number theory
*[[Euclideon]], an Australian computer graphics company

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[[Category:Mathematics disambiguation pages]]