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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 Log-polar coordinates ： ウィキペディア英語版 Log-polar coordinates In mathematics, log-polar coordinates (or logarithmic polar coordinates) is a coordinate system in two dimensions, where a point is identified by two numbers, one for the logarithm of the distance to a certain point, and one for an angle. Log-polar coordinates are closely connected to polar coordinates, which are usually used to describe domains in the plane with some sort of rotational symmetry. In areas like harmonic and complex analysis, the log-polar coordinates are more canonical than polar coordinates. == Definition and coordinate transformations == ''Log-polar coordinates'' in the plane consist of a pair of real numbers (ρ,θ), where ρ is the logarithm of the distance between a given point and the origin and θ is the angle between a line of reference (the ''x''-axis) and the line through the origin and the point. The angular coordinate is the same as for polar coordinates, while the radial coordinate is transformed according to the rule :$r\; =\; e^\backslash rho.\; \backslash ,$ where $r$ is the distance to the origin. The formulas for transformation from Cartesian coordinates to log-polar coordinates are given by :$\backslash begin\; \backslash rho\; =\; \backslash log\backslash sqrt,\; \backslash \backslash \; \backslash theta\; =\; \backslash arctan\; y/x\; \backslash hboxx>0.\; \backslash end$ and the formulas for transformation from log-polar to Cartesian coordinates are :$\backslash beginx\; =\; e^\backslash rho\backslash cos\backslash theta,\; \backslash \backslash \; y\; =\; e^\backslash rho\backslash sin\backslash theta.\backslash end$ By using complex numbers (''x'', ''y'') = ''x'' + ''iy'', the latter transformation can be written as :$x\; +\; iy\; =\; e^\; \backslash ,$ i.e. the complex exponential function. From this follows that basic equations in harmonic and complex analysis will have the same simple form as in Cartesian coordinates. This is not the case for polar coordinates. 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「Log-polar coordinates」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.