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In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz. The term was applied to a group of objects that arise from a common axiomatization of certain structures and split into three families, which were introduced separately: Möbius planes, Laguerre planes, and Minkowski planes.〔W. Benz, ''Vorlesungen über Geomerie der Algebren'', Springer (1973)〕 〔F. Buekenhout (ed.), ''Handbook of Incidence Geometry'', Elsevier (1995) ISBN 0-444-88355-X〕 == Möbius plane == (詳細はeuclidean plane and merging the set of lines with the set of circles to a set of blocks results in an inhomogeneous incidence structure: three distinct points determine one block, but lines are distinguishable as a set of blocks that pairwise mutually intersect at one point without being tangent (or no points when parallel). Adding to the point set the new point , defined to lie on every line results in every block being determined by exactly three points, as well as the intersection of any two blocks following a uniform pattern (intersecting at two points, tangent or non-intersecting). This homogeneous geometry is called classical inversive geometry or a Möbius plane. The inhomogeneity of the description (lines, circles, new point) can be seen to be non-substantive by using a 3-dimensional model. Using a stereographic projection, the classical Möbius plane may be seen to be isomorphic to the geometry of plane sections (circles) on a sphere in Euclidean 3-space. Analogously to the (axiomatic) projective plane, an (axiomatic) Möbius plane defines an incidence structure. Möbius planes may similarly be constructed over fields other than the real numbers. 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「Benz plane」の詳細全文を読む スポンサード リンク
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