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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 Coxeter's loxodromic sequence of tangent circles ： ウィキペディア英語版 Coxeter's loxodromic sequence of tangent circles In geometry, Coxeter's loxodromic sequence of tangent circles is an infinite sequence of circles arranged so that any four consecutive circles in the sequence are pairwise mutually tangent. This means that each circle in the sequence is tangent to the three circles that precede it and also to the three circles that follow it. The radii of the circles in the sequence form a geometric progression with ratio :$k=\backslash varphi\; +\; \backslash sqrt\; \backslash approx\; 2.89005\; \backslash \; ,$ where φ is the golden ratio. ''k'' and its reciprocal satisfy the equation :$(1+x+x^2+x^3)^2=2(1+x^2+x^4+x^6)\backslash \; ,$ and so any four consecutive circles in the sequence meet the conditions of Descartes' theorem. The centres of the circles in the sequence lie on a logarithmic spiral. Viewed from the centre of the spiral, the angle between the centres of successive circles is :$\backslash cos^\; \backslash left(\; \backslash frac\; \backslash right)\; \backslash approx\; 128.173\; ^\; \backslash circ\; \backslash \; .$ The construction is named after geometer Donald Coxeter, who generalised the two-dimensional case to sequences of spheres and hyperspheres in higher dimensions. ==See also== *Apollonian gasket 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「Coxeter's loxodromic sequence of tangent circles」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.