Euclidean
Encyclopedia
Euclidean relates to Euclid
(an ancient Greek mathematician), a town or others. It may refer to:
Geometry
Number theory
Other
See also
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
(an ancient Greek mathematician), a town or others. It may refer to:
Geometry
- Euclidean spaceEuclidean spaceIn mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions...
, the two-dimensional plane and three-dimensional space of Euclidean geometry as well as their higher dimensional generalizations. - Euclidean geometryEuclidean geometryEuclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
, the study of the properties of Euclidean spaces - Non-Euclidean geometryNon-Euclidean geometryNon-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
, systems of points, lines, and planes analogous to Euclidean geometry but without uniquely determined parallel lines - Euclidean distanceEuclidean distanceIn mathematics, the Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, and is given by the Pythagorean formula. By using this formula as distance, Euclidean space becomes a metric space...
, 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 algorithmEuclidean algorithmIn mathematics, the Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, also known as the greatest common factor or highest common factor...
, a method for finding greatest common divisors - Extended Euclidean algorithmExtended Euclidean algorithmThe extended Euclidean algorithm is an extension to the Euclidean algorithm. Besides finding the greatest common divisor of integers a and b, as the Euclidean algorithm does, it also finds integers x and y that satisfy Bézout's identityThe extended Euclidean algorithm is particularly useful when a...
, a method for solving the Diophantine equation ax + by = d where d is the greatest common divisor of a and b. - Euclidean domainEuclidean domainIn mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean algorithm...
, a system of numbers or values with properties similar enough to those of the integers to allow the extended Euclidean algorithm to work - Euclid's lemmaEuclid's lemmaIn mathematics, Euclid's lemma is an important lemma regarding divisibility and prime numbers. In its simplest form, the lemma states that a prime number that divides a product of two integers must divide one of the two integers...
: if a prime number divides a product of two numbers, then it divides at least one of those two numbers.
Other
- Euclidean relationEuclidean relationIn mathematics, Euclidean relations are a class of binary relations that satisfy a weakened form of transitivity that formalizes Euclid's "Common Notion 1" in The Elements: things which equal the same thing also equal one another.-Definition:...
, 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
See also
- Euclid (disambiguation)Euclid (disambiguation)Euclid was a Greek mathematician from Alexandria who authored Elements.The name has subsequently been used to refer to:-People:* Euclid of Alexandria, the ancient Greek mathematician and author of the Elements...
- Euclid's ElementsEuclid's ElementsEuclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...
, a 13-book mathematical treatise written by Euclid, that includes both geometry and number theory - The Euclidean division of the Intermediate Math League of Eastern MassachusettsIntermediate Math League of Eastern MassachusettsThe Intermediate Math League of Eastern Massachusetts is a math league for middle schools across Eastern Massachusetts. A brief history of IMLEM is given in its By-Laws:-Schools:...