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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 Dodecagon ： ウィキペディア英語版 Dodecagon In geometry, a dodecagon is any 12-sided polygon or 12-gon. ==Regular dodecagon== A ''regular dodecagon'' has Schläfli symbol and can be constructed as a truncated hexagon, t, or a twice-truncated triangle, tt. It has all sides of equal length and all angles equal to 150°. It has 12 lines of symmetry and rotational symmetry of order 12. Its Schläfli symbol is . The area of a regular dodecagon with side ''a'' is given by: : 3 \left(2+\sqrt \right) a^2 \\ & \simeq 11.19615242\,a^2. \end Or, if ''R'' is the radius of the circumscribed circle,〔See also Kürschák's geometric proof on (the Wolfram Demonstration Project )〕 :$A\; =\; 6\; \backslash sin\backslash left(\backslash frac\backslash right)\; R^2\; =\; 3\; R^2.$ And, if ''r'' is the radius of the inscribed circle, : 12 \left(2-\sqrt \right) r^2 \\ & \simeq 3.2153903\,r^2. \end A simple formula for area (given the two measurements) is: $\backslash scriptstyle\; A\backslash ,=\backslash ,3ad$ where ''d'' is the distance between parallel sides. Length ''d'' is the height of the dodecagon when it sits on a side as base, and the diameter of the inscribed circle. By simple trigonometry, $\backslash scriptstyle\; d\backslash ,=\backslash ,a(1\backslash ,+\backslash ,2cos\backslash ,+\backslash ,2cos)$. The perimeter for an inscribed dodecagon of radius 1 is 12√(2 - √3), or approximately 6.21165708246. 〔''Plane Geometry: Experiment, Classification, Discovery, Application'' by Clarence Addison Willis B., (1922) Blakiston's Son & Company, p. 249 ()〕 The perimeter for a circumscribed dodecagon of radius 1 is 24(2 – √3), or approximately 6.43078061835. Interestingly, this is double the value of the area of the ''inscribed'' dodecagon of radius 1. 〔''Elements of geometry'' by John Playfair, William Wallace, John Davidsons, (1814) Bell & Bradfute, p. 243 ()〕 With respect to the above-listed equations for area and perimeter, when the radius of the inscribed dodecagon is 1, note that the area of the inscribed dodecagon is 12(2 – √3) and the ''perimeter'' of this same inscribed dodecagon is 12√(2 - √3). 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「Dodecagon」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.