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parametrization theorem

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  • Modularity theorem — In mathematics the modularity theorem (formerly called the Taniyama–Shimura–Weil conjecture and several related names) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity …   Wikipedia

  • Hilbert's theorem (differential geometry) — In differential geometry, Hilbert s theorem (1901) states that there exists no complete regular surface S of constant negative Gaussian curvature K immersed in mathbb{R}^{3}. This theorem answers the question for the negative case of which… …   Wikipedia

  • Mean value theorem — For the theorem in harmonic function theory, see Harmonic function#Mean value property. Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables …   Wikipedia

  • Hilbert's Theorem 90 — In number theory, Hilbert s Theorem 90 (or Satz 90) refers to an important result on cyclic extensions of number fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it tells us that if L / K is a cyclic… …   Wikipedia

  • Plancherel theorem for spherical functions — In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its final form to Harish Chandra. It is a natural generalisation in non commutative harmonic… …   Wikipedia

  • Line integral — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

  • Surface integral — In mathematics, a surface integral is a definite integral taken over a surface (which may be a curved set in space); it can be thought of as the double integral analog of the line integral. Given a surface, one may integrate over it scalar fields …   Wikipedia

  • Differential geometry of curves — This article considers only curves in Euclidean space. Most of the notions presented here have analogues for curves in Riemannian and pseudo Riemannian manifolds. For a discussion of curves in an arbitrary topological space, see the main article… …   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

  • Curvature — In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this …   Wikipedia

  • Rotation representation (mathematics) — In geometry a rotation representation expresses the orientation of an object (or coordinate frame) relative to a coordinate reference frame. This concept extends to classical mechanics where rotational (or angular) kinematics is the science of… …   Wikipedia

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