euclidean

Englisch - Türkisch

Definition von euclidean im Englisch Türkisch wörterbuch: Öklit
Euclidean geometry: Öklit geometrisi
locally euclidean space: yerel öklit uzayı
non-euclidean: Öklid geometrisi ile ilişkili olmayan
Euclidian: {s} Öklit geometrisine ait
Euclidian: {s} Öklit ile ilgili

Englisch - Englisch

Definition von euclidean im Englisch Englisch wörterbuch: Adhering to the principles of traditional geometry, in which parallel lines are equidistant; Of or relating to Euclid's Elements, especially to Euclidean geometry; Alternative spelling of Euclidean; adj. Euclidean geometry Euclidean space non Euclidean geometry; {s} of or pertaining to Euclid or his work; Of or relating to Euclids Elements, especially to Euclidean geometry; relating to geometry as developed by Euclid; "Euclidian geometry"
Euclidean algorithm: A method based on the division algorithm for finding the greatest common divisor (gcd) of two given integers
Euclidean distance: The distance between two points defined as the square root of the sum of the squares of the differences between the corresponding coordinates of the points; for example, in two-dimensional Euclidean geometry, the Euclidean distance between two points a = (ax, ay) and b = (bx, by) is defined as:
Euclidean geometry: The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line
Euclidean group: the set of rigid motions that are also affine transformations
Euclidean metric: In the space \mathbb{R}^n, the metric d(\vec x, \vec y) = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2 + ... + (x_n - y_n)^2} where \vec x = (x_1, ..., x_n) and \vec y = (y_1, ..., y_n)
Euclidean plane: two-dimensional Euclidean space
Euclidean space: Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined
Euclidean space: Ordinary two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines
Euclidean spaces: plural form of Euclidean space
Euclidean geometry: Study of points, lines, angles, surfaces, and solids based on Euclid's axioms. Its importance lies less in its results than in the systematic method Euclid used to develop and present them. This axiomatic method has been the model for many systems of rational thought, even outside mathematics, for over 2,000 years. From 10 axioms and postulates, Euclid deduced 465 theorems, or propositions, concerning aspects of plane and solid geometric figures. This work was long held to constitute an accurate description of the physical world and to provide a sufficient basis for understanding it. During the 19th century, rejection of some of Euclid's postulates resulted in two non-Euclidean geometries that proved just as valid and consistent
Euclidean space: In geometry, a two-or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula. The only conception of physical space for over 2,000 years, it remains the most compelling and useful way of modeling the world as it is experienced. Though non-Euclidean spaces, such as those that emerge from elliptic geometry and hyperbolic geometry, have led scientists to a better understanding of the universe and of mathematics itself, Euclidean space remains the point of departure for their study
euclidean space: a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
non-Euclidean: of, or relating to non-Euclidean geometry
non-Euclidean geometries: plural form of non-Euclidean geometry
non-Euclidean geometry: Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common experience
Euclidian: {s} of or pertaining to Euclid or his work
euclidian: relating to geometry as developed by Euclid; "Euclidian geometry
euclidian: relating to geometry as developed by Euclid; "Euclidian geometry"
euclidian: Related to Euclid, or to the geometry of Euclid
non-Euclidean geometry: Any theory of the nature of geometric space differing from the traditional view held since Euclid's time. These geometries arose in the 19th century when several mathematicians working independently explored the possibility of rejecting Euclid's parallel postulate. Different assumptions about how many lines through a point not on a given line could be parallel to that line resulted in hyperbolic geometry and elliptic geometry. Mathematicians were forced to abandon the idea of a single correct geometry; it became their task not to discover mathematical systems but to create them by selecting consistent axioms and studying the theorems that could be derived from them. The development of these alternative geometries had a profound impact on the notion of space and paved the way for the theory of relativity. See also Nikolay Lobachevsky, Bernhard Riemann
non-euclidean geometry: geometry based on axioms different from Euclid's