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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 Philo line ： ウィキペディア英語版 Philo line In geometry, the Philo line is a line segment defined from an angle and a point. The Philo line for a point ''P'' that lies inside an angle with edges ''d'' and ''e'' is the shortest line segment that passes through ''P'' and has its endpoints on ''d'' and ''e''. Also known as the Philon line, it is named after Philo of Byzantium, a Greek writer on mechanical devices, who lived probably during the 1st or 2nd century BC. The Philo line is not, in general, constructible by compass and straightedge. == Doubling the cube == Philo's line can be used to double the cube, that is, to construct a geometric representation of the cube root of two, and this was Philo's purpose in defining this line (Coxeter and van de Craats, 1993). Specifically, let ''PQRS'' be a rectangle in which the aspect ratio ''PQ:QR'' is 1:2, as in the figure below. Let ''TU'' be the Philo line of point ''P'' with respect to right angle ''QRS''. Define point ''V'' to be the point of intersection of line ''TU'' and of the circle through points ''PQRS'', and let ''W'' be the point where line ''QR'' crosses a perpendicular line through ''V''. Then segments ''RS'' and ''RW'' are in proportion $\backslash scriptstyle\; 1:\backslash sqrt()$. In this figure, segments ''PU'' and ''VT'' are of equal length, and ''RV'' is perpendicular to ''TU''. These properties can be used as part of an equivalent alternative definition for the Philo line for a point ''P'' and angle edges ''d'' and ''e'': it is a line segment connecting ''d'' to ''e'' through ''P'' such that the distance along the segment from ''P'' to ''d'' is equal to the distance along the segment from ''V'' to ''e'', where ''V'' is the closest point on the segment to the corner point of the angle. Since doubling the cube is impossible with compass and straightedge, it is similarly impossible to construct the Philo line with these tools. 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「Philo line」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.