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• Euclidean_geometry abstract "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 (theorems) 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 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 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.".
• Euclidean_geometry thumbnail Sanzio_01_Euclid.jpg?width=300.
• Euclidean_geometry wikiPageExternalLink geometryunbound.
• Euclidean_geometry wikiPageID "9417".
• Euclidean_geometry wikiPageRevisionID "606505809".
• Euclidean_geometry hasPhotoCollection Euclidean_geometry.
• Euclidean_geometry id "p/e036350".
• Euclidean_geometry id "p/p072810".
• Euclidean_geometry sign "Bertrand Russell".
• Euclidean_geometry sign "Celia Hoyles".
• Euclidean_geometry sign "George Polyá".
• Euclidean_geometry sign "Padoa".
• Euclidean_geometry source "Essai d'une théorie algébrique des nombre entiers, avec une Introduction logique à une théorie déductive qulelconque".
• Euclidean_geometry source "How to Solve It, p. 208".
• Euclidean_geometry source "Mathematics and the metaphysicians".
• Euclidean_geometry source "The curricular shaping of students' approach to proof".
• Euclidean_geometry text "...when we begin to formulate the theory, we can imagine that the undefined symbols are completely devoid of meaning and that the unproved propositions are simply conditions imposed upon the undefined symbols. Then, the system of ideas that we have initially chosen is simply one interpretation of the undefined symbols; but..this interpretation can be ignored by the reader, who is free to replace it in his mind by another interpretation.. that satisfies the conditions... Logical questions thus become completely independent of empirical or psychological questions... The system of undefined symbols can then be regarded as the abstraction obtained from the specialized theories that result when...the system of undefined symbols is successively replaced by each of the interpretations...".
• Euclidean_geometry text "Geometry is the science of correct reasoning on incorrect figures.".
• Euclidean_geometry text "If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus, mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.".
• Euclidean_geometry text "If proof simply follows conviction of truth rather than contributing to its construction and is only experienced as a demonstration of something already known to be true, it is likely to remain meaningless and purposeless in the eyes of students.".
• Euclidean_geometry title "Euclidean geometry".
• Euclidean_geometry title "Plane trigonometry".
• Euclidean_geometry subject Category:Elementary_geometry.
• Euclidean_geometry subject Category:Euclidean_geometry.
• Euclidean_geometry subject Category:Greek_inventions.
• Euclidean_geometry type Ability105616246.
• Euclidean_geometry type Abstraction100002137.
• Euclidean_geometry type Cognition100023271.
• Euclidean_geometry type Creativity105624700.
• Euclidean_geometry type GreekInventions.
• Euclidean_geometry type Invention105633385.
• Euclidean_geometry type PsychologicalFeature100023100.
• Euclidean_geometry comment "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 (theorems) 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.".
• Euclidean_geometry label "Euclidean geometry".
• Euclidean_geometry label "Euclidische meetkunde".
• Euclidean_geometry label "Euklidische Geometrie".
• Euclidean_geometry label "Geometria euclidea".
• Euclidean_geometry label "Geometria euclidiana".
• Euclidean_geometry label "Geometria euklidesowa".
• Euclidean_geometry label "Geometría euclidiana".
• Euclidean_geometry label "Géométrie euclidienne".
• Euclidean_geometry label "Евклидова геометрия".
• Euclidean_geometry label "هندسة أقليدية".
• Euclidean_geometry label "ユークリッド幾何学".
• Euclidean_geometry label "欧几里得几何".
• Euclidean_geometry sameAs Eukleidovská_geometrie.
• Euclidean_geometry sameAs Euklidische_Geometrie.
• Euclidean_geometry sameAs Ευκλείδεια_γεωμετρία.
• Euclidean_geometry sameAs Geometría_euclidiana.
• Euclidean_geometry sameAs Euklidesen_axiomak.
• Euclidean_geometry sameAs Géométrie_euclidienne.
• Euclidean_geometry sameAs Geometri_Euklides.
• Euclidean_geometry sameAs Geometria_euclidea.
• Euclidean_geometry sameAs ユークリッド幾何学.
• Euclidean_geometry sameAs 유클리드_기하학.
• Euclidean_geometry sameAs Euclidische_meetkunde.
• Euclidean_geometry sameAs Geometria_euklidesowa.
• Euclidean_geometry sameAs Geometria_euclidiana.
• Euclidean_geometry sameAs m.02kvn.
• Euclidean_geometry sameAs Q162886.
• Euclidean_geometry sameAs Q162886.
• Euclidean_geometry sameAs Euclidean_geometry.
• Euclidean_geometry wasDerivedFrom Euclidean_geometry?oldid=606505809.
• Euclidean_geometry depiction Sanzio_01_Euclid.jpg.
• Euclidean_geometry isPrimaryTopicOf Euclidean_geometry.