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- In mathematics the symmetrization methods are algorithms of transforming a set to a ball with equal volume and centered at the origin. B is called the symmetrized version of A, usually denoted . These algorithms show up in solving the classical isoperimetric inequality problem, which asks: Given all two-dimensional shapes of a given area, which of them has the minimal perimeter (for details see Isoperimetric inequality). The conjectured answer was the disk and Steiner in 1838 showed this to be true using the Steiner symmetrization method (described below). From this many other isoperimetric problems sprung and other symmetrization algorithms. For example, Rayleigh's conjecture is that the first eigenvalue of the Dirichlet problem is minimized for the ball (see Rayleigh–Faber–Krahn inequality for details). Another problem is that the Newtonian capacity of a set A is minimized by and this was proved by Polya and G. Szego (1951) using circular symmetrization (described below). (en)
- Симметризация Штайнера — построение определённого типа, сопоставляющее произвольной фигуре фигуру с зеркальной симметрией.Это построение применяется при решении изопериметрической задачи,предложенном Якобом Штайнером в 1838. На основе симметризации Штайнера были построены и другие симметризации, которые используются в схожих задачах. (ru)
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- 8129 (xsd:nonNegativeInteger)
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- Симметризация Штайнера — построение определённого типа, сопоставляющее произвольной фигуре фигуру с зеркальной симметрией.Это построение применяется при решении изопериметрической задачи,предложенном Якобом Штайнером в 1838. На основе симметризации Штайнера были построены и другие симметризации, которые используются в схожих задачах. (ru)
- In mathematics the symmetrization methods are algorithms of transforming a set to a ball with equal volume and centered at the origin. B is called the symmetrized version of A, usually denoted . These algorithms show up in solving the classical isoperimetric inequality problem, which asks: Given all two-dimensional shapes of a given area, which of them has the minimal perimeter (for details see Isoperimetric inequality). The conjectured answer was the disk and Steiner in 1838 showed this to be true using the Steiner symmetrization method (described below). From this many other isoperimetric problems sprung and other symmetrization algorithms. For example, Rayleigh's conjecture is that the first eigenvalue of the Dirichlet problem is minimized for the ball (see Rayleigh–Faber–Krahn inequ (en)
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- Symmetrization methods (en)
- Симметризация Штайнера (ru)
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