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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク List of centroids ： ウィキペディア英語版 List of centroids The following diagrams show centroids of various two-dimensional objects. A centroid of an object $X$ in $n$-dimensional space is the intersection of all hyperplanes that divide $X$ into two parts of equal moment about the hyperplane. Informally, it is the "average" of all points of $X$. For an object of uniform composition (mass, density, etc.) the centroid of a body is also its centre of mass. In the case of two-dimensional objects shown below, the hyperplanes are simply lines. | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ |- |Quarter-circular area | align="center"| | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ |- |Semicircular area | align="center" | File:Semicircle centroid2.svg | align="center"|$\backslash ,\backslash !0$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ |- |Quarter-elliptical area | align="center" | | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ |- |Semielliptical area | align="center"| | align="center"|$\backslash ,\backslash !0$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ |- |Semiparabolic area |The area between the curve $y\; =\; \backslash frac\; x^2$ and the $\backslash ,\backslash !y$ axis, from $\backslash ,\backslash !x\; =\; 0$ to $\backslash ,\backslash !x\; =\; b$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ |- |Parabolic area |The area between the curve $\backslash ,\backslash !y\; =\; \backslash frac\; x^2$ and the line $\backslash ,\backslash !y\; =\; h$ | align="center"|$\backslash ,\backslash !0$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ |- |Parabolic spandrel |The area between the curve $\backslash ,\backslash !y\; =\; \backslash frac\; x^2$ and the $\backslash ,\backslash !x$ axis, from $\backslash ,\backslash !x\; =\; 0$ to $\backslash ,\backslash !x\; =\; b$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ |- |General spandrel |The area between the curve $y\; =\; \backslash frac\; x^n$ and the $\backslash ,\backslash !x$ axis, from $\backslash ,\backslash !x\; =\; 0$ to $\backslash ,\backslash !x\; =\; b$ | align="center"|$\backslash frac\; b$ | align="center"|$\backslash frac\; h$ | align="center"|$\backslash frac$ |- |Circular sector |The area between the curve (in polar coordinates) $\backslash ,\backslash !r\; =\; \backslash rho$ and the pole, from $\backslash ,\backslash !\backslash theta\; =\; -\backslash alpha$ to $\backslash ,\backslash !\backslash theta\; =\; \backslash alpha$ | align="center"|$\backslash frac$ | align="center"|$\backslash ,\backslash !0$ | align="center"|$\backslash ,\backslash !\backslash alpha\; \backslash rho^2$ |- |Circular segment | align="center"| | align="center"|$\backslash ,\backslash !0$ | align="center"|$\backslash frac\}\}$ | align="center"|$\backslash frac(\backslash theta\; -sin)$ |- |Quarter-circular arc |The points on the circle $\backslash ,\backslash !x^2\; +\; y^2\; =\; r^2$ and in the first quadrant | align="center"|$\backslash frac$ | align="center"|$\backslash frac$ | align="center"|$L=\backslash frac$ |- |Semicircular arc |The points on the circle $\backslash ,\backslash !x^2\; +\; y^2\; =\; r^2$ and above the $\backslash ,\backslash !x$ axis | align="center"|$\backslash ,\backslash !0$ | align="center"|$\backslash frac$ | align="center"|$L=\backslash ,\backslash !\backslash pi\; r$ |- |Arc of circle |The points on the curve (in polar coordinates) $\backslash ,\backslash !r\; =\; \backslash rho$, from $\backslash ,\backslash !\backslash theta\; =\; -\backslash alpha$ to $\backslash ,\backslash !\backslash theta\; =\; \backslash alpha$ | align="center"|$\backslash frac$ | align="center"|$\backslash ,\backslash !0$ | align="center"|$L=\backslash ,\backslash !2\backslash alpha\; \backslash rho$ |} ==External links== * http://www.engineering.com/Library/ArticlesPage/tabid/85/articleType/ArticleView/articleId/109/Centroids-of-Common-Shapes.aspx * http://www.efunda.com/math/areas/IndexArea.cfm 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「List of centroids」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.