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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 angle ： ウィキペディア英語版 Golden angle In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden section; that is, into two arcs such that the ratio of the length of the larger arc to the length of the smaller arc is the same as the ratio of the full circumference to the length of the larger arc. Algebraically, let ''a+b'' be the circumference of a circle, divided into a longer arc of length ''a'' and a smaller arc of length ''b'' such that :$\backslash frac\; =\; \backslash frac.$ The golden angle is then the angle subtended by the smaller arc of length ''b''. It measures approximately 137.5077640500378546463487 ...° or in radians 2.39996322972865332 ... . The name comes from the golden angle's connection to the golden ratio ''φ''; the exact value of the golden angle is : $360\backslash left(1\; -\; \backslash frac\backslash right)\; =\; 360(2\; -\; \backslash varphi)\; =\; \backslash frac\; =\; 180(3\; -\; \backslash sqrt)\backslash text$ or : $2\backslash pi\; \backslash left(\; 1\; -\; \backslash frac\backslash right)\; =\; 2\backslash pi(2\; -\; \backslash varphi)\; =\; \backslash frac\; =\; \backslash pi(3\; -\; \backslash sqrt)\backslash text,$ where the equivalences follow from well-known algebraic properties of the golden ratio. == Derivation == The golden ratio is equal to ''φ'' = ''a''/''b'' given the conditions above. Let ''ƒ'' be the fraction of the circumference subtended by the golden angle, or equivalently, the golden angle divided by the angular measurement of the circle. :$f\; =\; \backslash frac\; =\; \backslash frac.$ But since : $=\; \backslash varphi^2,$ it follows that :$f\; =\; \backslash frac$ This is equivalent to saying that ''φ'' 2 golden angles can fit in a circle. The fraction of a circle occupied by the golden angle is therefore :$f\; \backslash approx\; 0.381966.\; \backslash ,$ The golden angle ''g'' can therefore be numerically approximated in degrees as: :$g\; \backslash approx\; 360\; \backslash times\; 0.381966\; \backslash approx\; 137.508^\backslash circ,\backslash ,$ or in radians as : :$g\; \backslash approx\; 2\backslash pi\; \backslash times\; 0.381966\; \backslash approx\; 2.39996.\; \backslash ,$ 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 angle」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.