parametrized surface

parametrized surface
мат. параметризованная поверхность

Большой англо-русский и русско-английский словарь. 2001.

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  • Fréchet surface — In mathematics, a Fréchet surface is an equivalence class of parametrized surfaces in a metric space. In other words, a Fréchet surface is a way of thinking about surfaces independently of how they are written down (parametrized). The concept is… …   Wikipedia

  • Parametric surface — A parametric surface is a surface in the Euclidean space R3 which is defined by a parametric equation with two parameters. Parametric representation is the most general way to specify a surface. Surfaces that occur in two of the main theorems of… …   Wikipedia

  • Boy's surface — In geometry, Boy s surface is an immersion of the real projective plane in 3 dimensional space found by Werner Boy in 1901 (he discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3 space).… …   Wikipedia

  • Ruled surface — A hyperboloid of one sheet is a doubly ruled surface: it can be generated by either of two families of straight lines. In geometry, a surface S is ruled if through every point of S there is a straight line that lies on S. The most familiar… …   Wikipedia

  • Torsion tensor — In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet Serret formulas, for instance, quantifies the twist of a curve… …   Wikipedia

  • Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …   Wikipedia

  • Cartan connection — In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …   Wikipedia

  • Paraboloid — of revolution In mathematics, a paraboloid is a quadric surface of special kind. There are two kinds of paraboloids: elliptic and hyperbolic. The elliptic paraboloid is shaped like an oval cup and can have a maximum or minimum point. In a… …   Wikipedia

  • First fundamental form — In differential geometry, the first fundamental form is the inner product on the tangent space of a surface in three dimensional Euclidean space which is induced canonically from the dot product of R 3 . It permits the calculation of curvature… …   Wikipedia


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