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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 Chordal problem ： ウィキペディア英語版 Chordal problem In the book〔H. Croft, K. J. Falconer, and R. K. Guy. Unsolved Problems in Geometry, volume II of 'Problem Books in Mathematics'. Springer-Verlag, New York, Berlin, 1991.〕 there is a generalization of the equichordal point problem attributed to R. Gardner. :We consider a point $O$ inside a Jordan curve with the property that for any chord $()$ of the curve passing through $O$ the two parts $()$ and $()$ of the chord satisfy the following equation, where $\backslash alpha$ is a fixed real number: ::$$ |X-O|^\alpha+|O-Y|^\alpha = c 〔The Chordal Equation〕 where $c$ is a constant not depending on the chord. In this article we will call a point $O$ satisfying equation〔 a chordal point, or $\backslash alpha$-chordal point. The template for all chordal problems is this: :Problem: Is there a curve with two or more distinct points with this property? == Curves with one equichordal point == The center of the circle is a solution of the chordal equation〔 for an arbitrary $\backslash alpha$. One can show a continuum of solutions for many $\backslash alpha$, for example, $\backslash alpha=1$. The method of construction such solutions is by writing the equation of the curve in the form $r\; =\; f(\backslash theta)$ in polar coordinates. For $\backslash alpha=1$, the solution may be found in this article.〔Marek Rychlik, The Equichordal Point Problem, Electronic Research Announcements of the AMS, 1996, pages 108-123, available on-line at ()〕 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「Chordal problem」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.