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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 Radius of curvature (mathematics) ： ウィキペディア英語版 Radius of curvature (mathematics) In geometry, the radius of curvature, ''R'', of a curve at a point is a measure of the radius of the circular arc which best approximates the curve at that point. It is the inverse of the curvature. In the case of a space curve, the radius of curvature is the length of the curvature vector. In the case of a plane curve, then ''R'' is the absolute value of : $\backslash frac\; =\; \backslash frac,$ where ''s'' is the arc length from a fixed point on the curve, ''φ'' is the tangential angle and $\backslash scriptstyle\backslash kappa$ is the curvature. If the curve is given in Cartesian coordinates as ''y(x)'', then the radius of curvature is (assuming the curve is differentiable up to order 2): : $R\; =\backslash left|\; \backslash frac\; \}\backslash right|,$ \qquad\mbox\quad y' = \frac,\quad y'' = \frac, and | ''z'' | denotes the absolute value of ''z''. If the curve is given parametrically by functions ''x(t)'' and ''y(t)'', then the radius of curvature is :$R\; =\; \backslash ;\backslash left|\backslash frac\backslash right|\; \backslash ;=\; \backslash ;\backslash left|\backslash frac\; ^2\}\backslash big)^\}\; -\; \backslash dot\backslash ddot\}\backslash right|,$ \qquad\mbox\quad \dot = \frac,\quad\ddot = \frac,\quad \dot = \frac,\quad\ddot = \frac. Heuristically, this result can be interpreted as :$R\; =\; \backslash frac\; \backslash right|\},$ \qquad\mbox\quad \left| \mathbf \right| = \left| (\dot x, \dot y) \right| = R \frac. ==Examples== 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「Radius of curvature (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.