|
In geometry, the moment curve is an algebraic curve in ''d''-dimensional Euclidean space given by the set of points with Cartesian coordinates of the form :〔, Definition 5.4.1, p. 97; , Definition 1.6.3, p. 17.〕 In the Euclidean plane, the moment curve is a parabola, and in three-dimensional space it is a twisted cubic. Its closure in projective space is the rational normal curve. Moment curves have been used for several applications in discrete geometry including cyclic polytopes, the no-three-in-line problem, and a geometric proof of the chromatic number of Kneser graphs. ==Properties== Every hyperplane intersects the moment curve in a finite set of at most ''d'' points. If a hyperplane intersects the curve in exactly ''d'' points, then the curve crosses the hyperplane at each intersection point. Thus, every finite point set on the moment curve is in general linear position.〔, p. 100; , Lemma 5.4.2, p. 97; , Lemma 1.6.4, p. 17.〕 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「moment curve」の詳細全文を読む スポンサード リンク
|