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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 tetracontagon ： ウィキペディア英語版 tetracontagon In geometry, a tetracontagon or tessaracontagon is a forty-sided polygon or 40-gon.〔.〕〔(''The New Elements of Mathematics: Algebra and Geometry ) by Charles Sanders Peirce (1976), p.298〕 The sum of any tetracontagon's interior angles is 6840 degrees. ==Regular tetracontagon== A ''regular tetracontagon'' is represented by Schläfli symbol and can also be constructed as a truncated icosagon, t, which alternates two types of edges. Furthermore, it can also be constructed as a twice-truncated decagon, tt, or a thrice-truncated pentagon, ttt. One interior angle in a regular tetracontagon is 171°, meaning that one exterior angle would be 9°. The area of a regular tetracontagon is (with ) :$A\; =\; 10t^2\; \backslash cot\; \backslash frac$ and its inradius is :$r\; =\; \backslash fract\; \backslash cot\; \backslash frac$ The factor $\backslash cot\; \backslash frac$ is a root of the octic equation $x^\; -\; 8x^\; -\; 60x^\; -\; 8x^\; +\; 134x^\; +\; 8x^\; -\; 60x^\; +\; 8x\; +\; 1$. The circumradius of a regular tetracontagon is :$R\; =\; \backslash fract\; \backslash csc\; \backslash frac$ As 40 = 23 × 5, a regular tetracontagon is constructible using a compass and straightedge.〔(Constructible Polygon )〕 As a truncated icosagon, it can be constructed by an edge-bisection of a regular icosagon. This means that the values of $\backslash sin\; \backslash frac$ and $\backslash cos\; \backslash frac$ may be expressed in radicals as follows: :$\backslash sin\; \backslash frac\; =\; \backslash frac(\backslash sqrt-1)\backslash sqrt(2+\backslash sqrt)(5+\backslash sqrt)\}-\backslash frac\backslash sqrt)(\backslash sqrt-1)$ :$\backslash cos\; \backslash frac\; =\; \backslash frac(\backslash sqrt-1)\backslash sqrt-1)+\backslash frac(1+\backslash sqrt)\backslash sqrt(2-\backslash sqrt)(5+\backslash sqrt)\}$ 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「tetracontagon」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.