Parabolic geometry, former name for Euclidean geometry, a comprehensive and deductive mathematical system
Parabolic geometry (differential geometry): The homogeneous space defined by a semisimple Lie group modulo a parabolic subgroup, or the curved analog of such a space
Topics referred to by the same term
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Parabolicgeometry may refer to: Parabolicgeometry, former name for Euclidean geometry, a comprehensive and deductive mathematical system Parabolic geometry...
rarely used sequence elliptic geometry (spherical geometry), parabolicgeometry (Euclidean geometry), and hyperbolic geometry. In the former Soviet Union...
hyperbolic. The name "parabolic" is used because the assumption on the coefficients is the same as the condition for the analytic geometry equation A x 2 +...
obtain the parabolic cylinders with equations that can be written as: x 2 + 2 a y = 0. {\displaystyle x^{2}+2ay=0.} In projective geometry, a cylinder...
A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound...
In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by...
parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design...
adjusted parabolic troughs are generally designed with a lower concentration acceptance product. Parabolic trough concentrators have a simple geometry, but...
{p}}} ) is called a parabolic Cartan geometry, or simply a parabolicgeometry. A distinguishing feature of parabolicgeometries is a Lie algebra structure...
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...
In differential geometry, a smooth surface in three dimensions has a parabolic point when the Gaussian curvature is zero. Typically such points lie on...
Specific Brion, Michel. "Lectures on the geometry of flag varieties" (PDF). Popov, V.L. (2001) [1994], "Parabolic subgroup", Encyclopedia of Mathematics...
Picard theorem: maps from hyperbolic to parabolic to elliptic are easy, but maps from elliptic to parabolic or parabolic to hyperbolic are very constrained...
In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero as one or...
regarding parabolas, culminating in two proofs showing that the area of a parabolic segment (the region enclosed by a parabola and a line) is 4 3 {\displaystyle...
Ski geometry is the shape of the ski. Described in the direction of travel, the front of the ski, typically pointed or rounded, is the tip, the middle...
type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is...
In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola...
for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman abruptly quit his research job...
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean...
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