四维空间投影的垂直特性

本文系统地讨论了四维空间中相互垂直的几何元素的投影仍呈垂直关系的規律,当平行于某一超投影面的直线与任一直线(平面或超平面)垂直时,它们在该超投影面内的超投影仍然垂直。文章还讨论了相互垂直的两平面(或两超平面)、平面与超平面垂直时的投影规律,同时还举了几个例子以示其所得结论的应用。

PERPENDICULARITY PRINCIPLE OF PROJECTION IN FOUR-DIMENSIONAL SPACE

This paper systematically discusses the projections of geometrical elements perpendicular to each other remain perpendicular in four dimensional space and their low. It is concluded that if a line perpendicular to a line (plane or hyper-plane)in four dimensional space is parallel to a hyper-projective plane, their hyper-projections to that hyper-projective plane are perpendicular to each other.The projective rule of two planes(or hyperplanes) perpendicular to each other and a plane perpendicular to a hyperplane are also discussed, while some simple examples are given to illustrate the applications of these conclusions.