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In geometry, the Möbius–Kantor configuration is a configuration consisting of eight points and eight lines, with three points on each line and three lines through each point. It is not possible to draw points and lines having this pattern of incidences in the Euclidean plane, but it is possible in the complex projective plane. ==Coordinates== asked whether there exists a pair of polygons with ''p'' sides each, having the property that the vertices of one polygon lie on the lines through the edges of the other polygon, and vice versa. If so, the vertices and edges of these polygons would form a projective configuration. For ''p'' = 4 there is no solution in the Euclidean plane, but found pairs of polygons of this type, for a generalization of the problem in which the points and edges belong to the complex projective plane. That is, in Kantor's solution, the coordinates of the polygon vertices are complex numbers. Kantor's solution for ''p'' = 4, a pair of mutually-inscribed quadrilaterals in the complex projective plane, is called the Möbius–Kantor configuration. supplies the following simple complex projective coordinates for the eight points of the Möbius–Kantor configuration: :(1,0,0), (0,0,1), (ω, −1, 1), (−1, 0, 1), :(−1,ω2,1), (1,ω,0), (0,1,0), (0,−1,1), where ω denotes the complex cube root of 1. 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「Möbius–Kantor configuration」の詳細全文を読む スポンサード リンク
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