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Euclidean (or, less commonly, Euclidian) is an adjective derived from the name of Euclid, an ancient Greek mathematician.
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
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
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Euclidean geometry - Wikipedia
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.Euclid's approach consists in …
Euclidean geometry | Definition, Axioms, & Postulates | Britannica
09 Jan 2025 · Euclidean geometry is the study of plane and solid figures on the basis of axioms and theorems employed by the ancient Greek mathematician Euclid. The term refers to the …
Euclidean - Wikipedia
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 …
Euclidean space - Wikipedia
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but …
Euclidean Definition & Meaning - Merriam-Webster
The meaning of EUCLIDEAN is of, relating to, or based on the geometry of Euclid or a geometry with similar axioms.
What is Euclidean Geometry | Definition, Axioms
10 Jun 2024 · Euclid's geometry, also known as Euclidean geometry, is a foundational system in mathematics. It deals with the properties of points, lines, planes, and solids based on a set of …
Euclidean Geometry (Definition, Facts, Axioms and Postulates)
Euclidean geometry is a study of plane geometry in two dimensions based on axioms, theorems and postulates. Applications of Euclidean geometry in real life, examples at BYJU’S.
Euclids Geometry - Definition, Axioms, Postulates, Examples, …
Euclid's Geometry, also known as Euclidean Geometry, is considered the study of plane and solid shapes based on different axioms and theorems. The word Geometry comes from the Greek …
Euclidean -- from Wolfram MathWorld
20 Jan 2025 · The Euclidean geometry of the plane (Books I-IV) and of the three-dimensional space (Books XI-XIII) is based on five postulates, the first four of which are about the basic …
The Foundations of Euclidean Geometry: A Comprehensive Guide
24 Okt 2024 · Euclidean geometry teaches that the sum of the interior angles of a triangle is always 180 degrees. This result is fundamental to the study of polygons and is used in …