翻訳と辞書 Words near each other ・ Annulobalcis cicatricosa ・ Annulobalcis maculatus ・ Annulobalcis marshalli ・ Annulobalcis pellucida ・ Annulobalcis procera ・ Annulobalcis shimazui ・ Annulobalcis vinarius ・ Annulobalcis wareni ・ Annulobalcis yamamotoi ・ Annuloceras ・ Annulohypoxylon ・ Annulohypoxylon archeri ・ Annulus ・ Annulus (botany) ・ Annulus (firestop) ・ Annulus (mathematics) ・ Annulus (mycology) ・ Annulus (oil well) ・ Annulus (zoology) ・ Annulus fibrosus ・ Annulus of Zinn ・ Annulus theorem ・ Annulusmagnus ・ Annulyne ・ Annum ingressi ・ Annum Innum Ennum ・ Annum sacrum ・ Annunciade ・ Annunciation ・ Annunciation (Ambrogio Lorenzetti) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Annulus (mathematics) ： ウィキペディア英語版 Annulus (mathematics) In mathematics, an annulus (the Latin word for "little ring", with plural ''annuli'') is a ring-shaped object, especially a region bounded by two concentric circles. The adjectival form is annular (as in annular eclipse). The open annulus is topologically equivalent to both the open cylinder and the punctured plane. Informally, it has the shape of a hardware washer. The area of an annulus is the difference in the areas of the larger circle of radius and the smaller one of radius : :$A\; =\; \backslash pi\; R^2\; -\; \backslash pi\; r^2\; =\; \backslash pi(R^2\; -\; r^2)\backslash ,.$ The area of an annulus can be obtained from the length of the longest interval that can lie completely inside the annulus, 2 *''d'' in the accompanying diagram. This can be proven by the Pythagorean theorem; the length of the longest interval that can lie completely inside the annulus will be tangent to the smaller circle and form a right angle with its radius at that point. Therefore, ''d'' and ''r'' are the sides of a right angled triangle with hypotenuse ''R'' and the area is given by: :$A\; =\; \backslash pi\backslash left(R^2\; -\; r^2\backslash right)\; =\; \backslash pi\; d^2\; \backslash ,.$ The area can also be obtained via calculus by dividing the annulus up into an infinite number of annuli of infinitesimal width and area and then integrating from ''ρ'' = ''r'' to ''ρ'' = ''R'': :$A\; =\; \backslash int\_r^R\; 2\backslash pi\backslash rho\backslash ,\; d\backslash rho\; =\; \backslash pi\backslash left(R^2\; -\; r^2\backslash right).$ The area of an annulus sector of angle , with measured in radians, is given by: :$A\; =\; \backslash frac\; \backslash left(R^2\; -\; r^2\backslash right)$ ==Complex structure== In complex analysis an annulus in the complex plane is an open region defined by: : If is , the region is known as the punctured disk of radius around the point . As a subset of the complex plane, an annulus can be considered as a Riemann surface. The complex structure of an annulus depends only on the ratio . Each annulus can be holomorphically mapped to a standard one centered at the origin and with outer radius by the map :$z\; \backslash mapsto\; \backslash frac.$ The inner radius is then . The Hadamard three-circle theorem is a statement about the maximum value a holomorphic function may take inside an annulus. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Annulus (mathematics)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.