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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 Kepler triangle ： ウィキペディア英語版 Kepler triangle A Kepler triangle is a right triangle with edge lengths in geometric progression. The ratio of the edges of a Kepler triangle is linked to the golden ratio :$\backslash varphi\; =$ and can be written: $1\; :\; \backslash sqrt\backslash varphi\; :\; \backslash varphi$, or approximately 1 : 1.272 : 1.618. The squares of the edges of this triangle (see figure) are in geometric progression according to the golden ratio. Triangles with such ratios are named after the German mathematician and astronomer Johannes Kepler (1571–1630), who first demonstrated that this triangle is characterised by a ratio between short side and hypotenuse equal to the golden ratio. Kepler triangles combine two key mathematical concepts—the Pythagorean theorem and the golden ratio—that fascinated Kepler deeply, as he expressed in this quotation: Some sources claim that a triangle with dimensions closely approximating a Kepler triangle can be recognized in the Great Pyramid of Giza.〔(Squaring the circle, Paul Calter )〕 ==Derivation== The fact that a triangle with edges $1$, $\backslash sqrt\backslash varphi$ and $\backslash varphi$, forms a right triangle follows directly from rewriting the defining quadratic polynomial for the golden ratio $\backslash varphi$: :$\backslash varphi^2\; =\; \backslash varphi\; +\; 1$ into the form of the Pythagorean theorem: :$(\backslash varphi)^2\; =\; (\backslash sqrt\backslash varphi)^2\; +\; (1)^2.$ 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「Kepler triangle」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.