Definitions for euclidean geometry
This page provides all possible meanings and translations of the word euclidean geometry
Random House Webster's College Dictionary
geometry based upon the postulates of Euclid, esp. the postulate that only one line may be drawn through a given point parallel to a given line.
Origin of Euclidean geometry:
elementary geometry, parabolic geometry, Euclidean geometry(noun)
(mathematics) geometry based on Euclid's axioms
The familiar geometry of the real world, based on the postulate that through any two points there is exactly one straight line.
Euclidean 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. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. For over two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only where the gravitational field is weak.
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