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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 Golden spiral ： ウィキペディア英語版 Golden spiral In geometry, a golden spiral is a logarithmic spiral whose growth factor is , the golden ratio.〔Chang, Yu-sung, "(Golden Spiral )", The Wolfram Demonstrations Project.〕 That is, a golden spiral gets wider (or further from its origin) by a factor of for every quarter turn it makes. ==Formula== The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor : :$r\; =\; ae^\backslash ,$ or :$\backslash theta\; =\; \backslash frac\; \backslash ln(r/a),$ with being the base of Natural Logarithms, being an arbitrary positive real constant, and such that when is a right angle (a quarter turn in either direction): :$e^\; \backslash over\; \backslash theta\_\backslash mathrm\}.$ The numerical value of depends on whether the right angle is measured as 90 degrees or as $\backslash textstyle\backslash frac$ radians; and since the angle can be in either direction, it is easiest to write the formula for the absolute value of $b$ (that is, can also be the negative of this value): :$|b|\; =\; \backslash doteq\; 0.0053468\backslash ,$ for in degrees; :$|b|\; =\; \backslash doteq\; 0.3063489\backslash ,$ for in radians . An alternate formula for a logarithmic and golden spiral is: :$r\; =\; ac^\backslash ,$ where the constant is given by: :$c\; =\; e^b\backslash ,$ which for the golden spiral gives values of: :$c\; =\; \backslash varphi\; ^\; \backslash frac\; \backslash doteq\; 1.0053611$ if is measured in degrees, and :$c\; =\; \backslash varphi\; ^\; \backslash frac\; \backslash doteq\; 1.358456.$ if is measured in radians. 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「Golden spiral」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.