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Qué (quién) es Euclidean geometry - definición
Euclidean geometry
![A disproof of Euclidean geometry as a description of physical space. In a 1919 test of the general theory of relativity, stars (marked with short horizontal lines) were photographed during a solar [[eclipse]]. The rays of starlight were bent by the Sun's gravity on their way to Earth. This is interpreted as evidence in favor of Einstein's prediction that gravity would cause deviations from Euclidean geometry.](https://commons.wikimedia.org/wiki/Special:FilePath/1919 eclipse negative.jpg?width=200 "A disproof of Euclidean geometry as a description of physical space. In a 1919 test of the general theory of relativity, stars (marked with short horizontal lines) were photographed during a solar [[eclipse]]. The rays of starlight were bent by the Sun's gravity on their way to Earth. This is interpreted as evidence in favor of Einstein's prediction that gravity would cause deviations from Euclidean geometry.")
![invariant]]s and studying them is the essence of geometry.](https://commons.wikimedia.org/wiki/Special:FilePath/Congruentie.svg?width=200 "invariant]]s and studying them is the essence of geometry.")
![René Descartes. Portrait after [[Frans Hals]], 1648.](https://commons.wikimedia.org/wiki/Special:FilePath/Frans Hals - Portret van René Descartes.jpg?width=200 "René Descartes. Portrait after [[Frans Hals]], 1648.")
![Squaring the circle: the areas of this square and this circle are equal. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized [[compass and straightedge]].](https://commons.wikimedia.org/wiki/Special:FilePath/Squaring the circle.svg?width=200 "Squaring the circle: the areas of this square and this circle are equal. In 1882, it was proven that this figure cannot be constructed in a finite number of steps with an idealized [[compass and straightedge]].")
![The ''[[pons asinorum]]'' or ''bridge of asses theorem'' states that in an isosceles triangle, α = β and γ = δ.](https://commons.wikimedia.org/wiki/Special:FilePath/pons_asinorum_dzmanto.png?width=200 "The ''[[pons asinorum]]'' or ''bridge of asses theorem'' states that in an isosceles triangle, α = β and γ = δ.")
![The ''[[Pythagorean theorem]]'' states that the sum of the areas of the two squares on the legs (''a'' and ''b'') of a right triangle equals the area of the square on the hypotenuse (''c'').](https://commons.wikimedia.org/wiki/Special:FilePath/Pythagorean.svg?width=200 "The ''[[Pythagorean theorem]]'' states that the sum of the areas of the two squares on the legs (''a'' and ''b'') of a right triangle equals the area of the square on the hypotenuse (''c'').")
![''[[Thales' theorem]]'' states that if AC is a diameter, then the angle at B is a right angle.](https://commons.wikimedia.org/wiki/Special:FilePath/Thales' Theorem Simple.svg?width=200 "''[[Thales' theorem]]'' states that if AC is a diameter, then the angle at B is a right angle.")
![level]]](https://commons.wikimedia.org/wiki/Special:FilePath/us land survey officer.jpg?width=200 "level]]")
![orange]]s.](https://commons.wikimedia.org/wiki/Special:FilePath/Ambersweet oranges.jpg?width=200 "orange]]s.")
MATHEMATICAL SYSTEM ATTRIBUTED TO EUCLID
Geometry in R2; Euclid's postulates; Plane Geometry; Euclidean Geometry; Euclidian geometry; Geometry Postulates; Two dimensional geometry; Two-dimensional geometry; Noncoordinate geometry; Orthogonal geometry; Euclid's axioms; Euclidean geometry of the plane; Euclid axioms; Euclid postulates; Euclidean axioms; Axioms of geometry; Euclidean plane geometry; Fundamental concepts of geometry; Plane geometry; Classical geometry; Planar geometry; Geometry of Euclid; Euclid's second postulate; Euclid's third postulate; Euclid's fourth postulate; Applications of Euclidean geometry; 2D 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.
Non-Euclidean geometry
.jpg?width=200 "On a sphere, the sum of the angles of a triangle is not equal to 180°. The surface of a sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is very nearly 180°.")
TWO GEOMETRIES BASED ON AXIOMS CLOSELY RELATED TO THOSE SPECIFYING EUCLIDEAN GEOMETRY
Non-euclidean geometries; NonEuclidean geometry; Non-Euclidean; Noneuclidean geometry; Non-Euclidian geometry; Non-Euclidean geometries; Non-euclidian geometry; Models of non-Euclidean geometry; Non-Euclidena geometry; Non-Euclidean space; Non-Euclidean Geometry; Non euclidian geometry; Models of Non-Euclidean geometry; Non-euclidean Geometry; Non-euclidean geometry; History of non-Euclidean geometry; Kinematic geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.
Models of non-Euclidean geometry
TWO GEOMETRIES BASED ON AXIOMS CLOSELY RELATED TO THOSE SPECIFYING EUCLIDEAN GEOMETRY
Non-euclidean geometries; NonEuclidean geometry; Non-Euclidean; Noneuclidean geometry; Non-Euclidian geometry; Non-Euclidean geometries; Non-euclidian geometry; Models of non-Euclidean geometry; Non-Euclidena geometry; Non-Euclidean space; Non-Euclidean Geometry; Non euclidian geometry; Models of Non-Euclidean geometry; Non-euclidean Geometry; Non-euclidean geometry; History of non-Euclidean geometry; Kinematic geometry
Models of non-Euclidean geometry are mathematical models of geometries which are non-Euclidean in the sense that it is not the case that exactly one line can be drawn parallel to a given line l through a point that is not on l. In hyperbolic geometric models, by contrast, there are infinitely many lines through A parallel to l, and in elliptic geometric models, parallel lines do not exist.
Ejemplos de uso de Euclidean geometry
1. "If kids can play Dungeons and Dragons, if they can understand the universe of Lord of the Rings, where the world is created from a few rules, then they can comprehend physics, where everything is based on three of Newton‘s laws, or Euclidean geometry, where everything is based on five basic axioms." She maintains, moreover, that in the same way that nature abhors a vacuum, an adolescent mind left intellectually idle will find something else to do, often with undesirable results.