Definitions for euclidean geometry
eu·clidean ge·om·e·t·ry

Princeton's WordNetRate this definition:0.0 / 0 votes

1. elementary geometry, parabolic geometry, Euclidean geometrynoun

   (mathematics) geometry based on Euclid's axioms

WiktionaryRate this definition:2.0 / 1 vote

1. Euclidean geometrynoun

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

WikipediaRate this definition:0.0 / 0 votes

1. Euclidean geometry

   Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. 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 more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) 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 Albert Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only over short distances (relative to the strength of the gravitational field).Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects. This is in contrast to analytic geometry, introduced almost 2,000 years later by René Descartes, which uses coordinates to express geometric properties as algebraic formulas.

ChatGPTRate this definition:0.0 / 0 votes

1. euclidean geometry

   Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid. This form of geometry is based on a system of postulates or axioms perceived as obvious truths, from which theorems are logically derived. The key postulates include concepts such as: a straight line can be drawn from any two points, a finite line can be extended indefinitely along a straight line, a circle may be drawn with any given radius at any center, and all right angles are equal. Euclidean geometry is commonly considered the traditional form of geometry taught in many schools, covering concepts like points, lines, angles, triangles, and circles.

WikidataRate this definition:0.0 / 0 votes

1. Euclidean geometry

   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.

Matched Categories

1. • Geometry
   • Mathematics

How to pronounce euclidean geometry?

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How to say euclidean geometry in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of euclidean geometry in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of euclidean geometry in Pythagorean Numerology is: 2

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=euclidean geometry
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Euclidean_Geometry
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Euclidean_Geometry
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=euclidean geometry