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isoperimetric theorem

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  • Isoperimetric inequality — The isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. Isoperimetric literally means… …   Wikipedia

  • Isoperimetric dimension — In mathematics, the isoperimetric dimension of a manifold is a notion of dimension that tries to capture how the large scale behavior of the manifold resembles that of a Euclidean space (unlike the topological dimension or the Hausdorff dimension …   Wikipedia

  • Brunn-Minkowski theorem — In mathematics, the Brunn Minkowski theorem (or Brunn Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn Minkowski theorem (H …   Wikipedia

  • Busemann's theorem — In mathematics, Busemann s theorem is a theorem in Euclidean geometry and geometric tomography. It was first proved by Herbert Busemann in 1949 and was motivated by his theory of area in Finsler spaces.tatement of the theoremLet K be a convex… …   Wikipedia

  • Berger-Kazdan comparison theorem — In mathematics, the Berger Kazdan comparison theorem is a result in Riemannian geometry that gives a lower bound on the volume of a Riemannian manifold and also gives a necessary and sufficient condition for the manifold to be isometric to the m… …   Wikipedia

  • Saint-Venant's theorem — In solid mechanics, it is common to analyze the properties of beams with constant cross section. Saint Venant s theorem states that the simply connected cross section with maximal torsional rigidity is a circle. E. Makai, A proof of Saint Venant… …   Wikipedia

  • Gerrymandering — Jerrymander redirects here. Jerrymander may also refer to the arachnid known as Solifugae. For the 2010 documentary film, see Gerrymandering (film). Part of the Politics series …   Wikipedia

  • List of theorems — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… …   Wikipedia

  • List of geometry topics — This is list of geometry topics, by Wikipedia page.*Geometric shape covers standard terms for plane shapes *List of mathematical shapes covers all dimensions *List of differential geometry topics *List of geometers *See also list of curves, list… …   Wikipedia

  • Quadrilateral — This article is about four sided mathematical shapes. For other uses, see Quadrilateral (disambiguation). Quadrilateral Six different types of quadrilaterals Edges and vertices 4 …   Wikipedia

  • Rectangle — Family Orthotope Type Quadrilateral Edges and vertices 4 Schläfli symbol {}x{} …   Wikipedia

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