两类特殊二次直纹面的新定义

New Definitions for Two Kinds of Special Quadric Ruled Surface

二次直纹面是空间解解析几何的主要內容之一,二次直纹面分为退化的二次直纹面和非退化的二次直纹面,非退化的二次直纹面有单叶双曲面、双曲抛物面以及二次柱面、二次锥面.《解析几何》教科书中只柱面、锥面用动母线的形式给出其参数方程。因此该文在先用动母线的形式给出了单叶双曲面与双曲抛物面的一种参数方程的基础上,讨论了此参数方程中两族坐标曲线的曲率和挠率。

Quadfic ruled surface is one of the most important contents in space analytic geometry. Quadric ruled surfaces are divided into degenerated quadrie ruled surface and the non - degenerated quadric ruled surface. The non- degenerated quadfic ruled surfaces include the uniparted hyperboloid, the hyperbolic paraboloid, the quadric cylinder and the quadfic cone. In the textbook Analytic Geometry, only the cylinder and the conical surface give their parametric equations in the form of restrained bus bar. Therefore, this article first gives out the parametric equation of the uniparted hyperboloid and the hyperbolic paraboloid in the form of restrained bus bar, and then discusses the curvature and the torsion of two races of the coordinate curve in this parametric equation.