四维空间直线绕平面的旋转

REVOLUTION OF A LINE ABOUT A PLANE IN FOUR-DIMENSIONAL SPACE

本文对四维空间直线绕平面旋转的轨迹进行一投详尽的讨论，按照直线与“轴平面”的相对位置不同，该旋转轨迹分别为圆柱面、圆锥面和单叶回转双曲面，并认为这些回转曲面的轴线是过该直线的与“轴平面”垂直的超平面与“轴平面”的交线。

In this paper,the problem of the revolution trace of a line about a plane in four-dimen-sional space is discussed in detail.In accordance with the different positions of the generatrix to the axis plane,the revolution trace is respectively a cylinder,a cone and a hyperboloid of revolution of One sheet.The axis of the surface of revolution is the line of interaction of the axis plane,with the hyperplane which contains the generatrix and is perpendicular to the“axis plane”.