翻訳と辞書 Words near each other ・ Quadratic residuosity problem ・ Quadratic set ・ Quadratic sieve ・ Quadratic transformation ・ Quadratic unconstrained binary optimization ・ Quadratic variation ・ Quadratic-linear algebra ・ Quadratically closed field ・ Quadratically constrained quadratic program ・ Quadratics ・ Quadratini ・ Quadratino ・ Quadrato di Villafranca ・ Quadratojugal bone ・ Quadratrix ・ Quadratrix of Hippias ・ Quadratur des Kreises ・ Quadrature ・ Quadrature (astronomy) ・ Quadrature (mathematics) ・ Quadrature amplitude modulation ・ Quadrature based moment methods ・ Quadrature booster ・ Quadrature division multiple access ・ Quadrature domains ・ Quadrature filter ・ Quadrature mirror filter ・ Quadrature modulation ・ Quadratus ・ Quadratus (martyr) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quadratrix of Hippias ： ウィキペディア英語版 Quadratrix of Hippias The quadratrix or trisectrix of Hippias (also quadratrix of Dinostratos) is a curve, which is created by a uniform motion. It is one of the oldest examples for a kinematic curve, that is a curve created through motion. Its discovery is attributed to the Greek sophist Hippias of Elis, who used it around 420 BC in an attempt to solve the angle trisection problem (hence trisectrix). Later around 350 BC Dinostratus used it in an attempt to solve the problem of squaring the circle (hence quadratrix). == Definition == Consider a square ''ABCD'' with an inscribed quarter circle centered in ''A'', such that the side of the square is the circle's radius. Let ''E'' be a point that travels with a constant angular velocity on the quarter circle arc from ''D'' to ''B''. In addition the point ''F'' travels with a constant velocity from ''D'' to ''A'' on the line segment , in such away that ''E'' and ''F'' start at the same time at ''D'' and arrive at the same time in ''B'' and ''D''. Now the quadratrix is defined as the locus of the intersection of the parallel to through ''F'' and the line segment .〔〔 If one places such a square ''ABCD'' with side length ''a'' in a (cartesian) coordinate system with the side on the ''x''-axis and vertex ''A'' in the origin, then the quadratix is described by a planar curve $\backslash gamma:(0,\backslash tfrac]\backslash rightarrow\; \backslash mathbb^2$ with: ::$\backslash gamma(t)=\backslash beginx(t)\backslash \backslash y(t)\backslash end=\backslash begin\backslash frac\; t\backslash cot(t)\backslash \backslash \backslash frac\; t\backslash end$ This description can also be used to give an analytical rather than a geometric definition of the quadratrix and to extend it beyond the $(0,\backslash tfrac]$ interval. It does however remain undefined at the singularities of $\backslash cot(t)$ except for the case of $t=0$, where due to $\backslash lim\_\; t\; \backslash cot(t)=1$ the singularity is removable and hence yields a continuous planar curve on the interval $(-\backslash pi,\backslash pi)$ 〔〔 To describe the quadratrix as simple function rather than planar curve, it is advantageous to switch the ''y''-axis and the ''x''-axis, that is to place the side on ''y''-axis rather than on the ''x''-axis. Then the quadratrix is given by the following function ''f''(x):〔〔 ::$f(x)=x\; \backslash cdot\; \backslash cot\; \backslash left(\backslash frac\; \backslash cdot\; x\; \backslash right)$ 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「Quadratrix of Hippias」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.