euclidean geometry

English - Turkish

Definition of euclidean geometry in English Turkish dictionary

Öklit geometrisi

Öklid geometrisi

English - English

Definition of euclidean geometry in English English dictionary

The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line

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

Related Terms

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

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

Hyphenation

Eu·clid·e·an ge·o·me·try