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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 Regular pentagon ： ウィキペディア英語版 Pentagon In geometry, a pentagon (from the Greek πέντε ''pente'' and γωνία ''gonia'', meaning ''five'' and ''angle''〔"pentagon, adj. and n." OED Online. Oxford University Press, June 2014. Web. 17 August 2014.〕) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting ''regular pentagon'' (or ''star pentagon'') is called a pentagram. ==Regular pentagons== A ''regular pentagon'' has Schläfli symbol and interior angles are 108°. A ''regular pentagon'' has five lines of reflectional symmetry, and rotational symmetry of order 5 (through 72°, 144°, 216° and 288°). The diagonals of a convex regular pentagon are in the golden ratio to its sides. Its height (distance from one side to the opposite vertex) and width (distance between two farthest separated points, which equals the diagonal length) are given by :$\backslash text\; =\; \backslash frac\; \backslash cdot\; \backslash text\backslash approx\; 1.539\; \backslash cdot\; \backslash text,$ :$\backslash text\; =\; \backslash text=\; \backslash frac\; \backslash cdot\; \backslash text\backslash approx\; 1.618\; \backslash cdot\; \backslash text,$ :$\backslash text\; =\; R\backslash \; \}\; \}\; =\; 2R\backslash cos\; 18^\backslash circ\; =\; 2R\backslash cos\backslash frac\; \backslash approx\; 1.902\; R,$ where ''R'' is the radius of the circumcircle. The area of a convex regular convex pentagon with side length ''t'' is given by :$A\; =\; \backslash frac\; =\; \backslash frac\; \backslash approx\; 1.720\; t^2.$ A pentagram or pentangle is a regular star pentagon. Its Schläfli symbol is . Its sides form the diagonals of a regular convex pentagon – in this arrangement the sides of the two pentagons are in the golden ratio. When a regular pentagon is inscribed in a circle with radius ''R'', its edge length ''t'' is given by the expression :$t\; =\; R\backslash \; \}\; \}\; =\; 2R\backslash sin\; 36^\backslash circ\; =\; 2R\backslash sin\backslash frac\; \backslash approx\; 1.176\; R,$ and its area is :$A=\backslash frac\backslash sqrt\};$ since the area of the circumscribed circle is $\backslash pi\; R^2,$ the regular pentagon fills approximately 0.7568 of its circumscribed circle. 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「Pentagon」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.