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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 Semicubical parabola ： ウィキペディア英語版 Semicubical parabola In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve defined parametrically as〔.〕 :$x\; =\; t^2\; \backslash ,$ :$y\; =\; at^3.\; \backslash ,$ Its implicit equation is :$y^2-a^2x^3=0,$ which can be solved in to yield the equation〔 :$y\; =\; \backslash pm\; ax^.$ This cubic curve has a singular point at the origin, which is a cusp. If one sets , , and , one gets :$X\; =\; u^2$ :$Y\; =\; u^3.$ This implies that, for any value of , the curve is homothetic to the curve for which , or, equivalently, that the curves corresponding to different values of differ only by the choice of the unit length. ==Properties== A special case of the semicubical parabola is the evolute of the parabola.〔 It has the equation :$x\; =\; (2y)^\; +\; .$ Expanding the Tschirnhausen cubic catacaustic shows that it is also a semicubical parabola: :$x\; =\; 3(t^2\; -\; 3)\; =\; 3t^2\; -\; 9\backslash ,$ :$y\; =\; t(t^2\; -\; 3)\; =\; t^3\; -\; 3t.\backslash ,$ An additional defining property of the semicubical parabola is that it is an isochrone curve, meaning that a particle following its path while being pulled down by gravity travels equal vertical intervals in equal time periods. In this way it is related to the tautochrone curve, for which particles at different starting points always take equal time to reach the bottom, and the brachistochrone curve, the curve that minimizes the time it takes for a falling particle to travel from its start to its end.〔 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「Semicubical parabola」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.