四维配极原理

The Polar Theories of Four Dimensions

现有的射影几何学中,二维空间里的极点、极线间的配极对应,三维空间里的反配极对应和直线与平面的正交配极对应等原理,可以用于在按蒙若法反映在二维平面上的中心投影里,直接解决直线与平面这两个元素之间,已知一个元素求作另一垂直元素的问题。本文在此基础上提出了四维空间里的配极对应,反配极对应和正交配极对应等理论,用解析法研究了它们的有关特性并导出了有关的计算公式,为在四维点中心中心投影按蒙若法反映的超投影面里,解决直线、平面和超平面中任意两个元素的垂直问题,提供了理论基础。

In projective geometry, the polar correspon-dence between polar point and polarline in two- dimensionalspace, the theories of inverse polar correspondence aud theorthogonal polar. Correspondence between lines and planes inthree-dimensional space can be used disectly to determine anelement perpendicular to the other element between a line and aplane of central projection in two dimensional space, press-ented on a plane witn the method of Monge.Based on the known theory. this paper presents the theoriesof four-dimensional polar correspondence, inverse polarcorrespondence and orthogonal polar correspondence. Theirroperties are studied by analytic demonstration and therelated formulas are derived. This provides the basic theoriesfor determining the problems of perpendicular about any twoelements of line,plane and hyperplane of central projectionwith a point as projecting center in four-dimensional space,presented on a hyperplane of projection with the method ofMonge.