二次曲面直纹性学习要点剖析

An Analysis on the Keys to Learning the Property of the Straight Line Formed Quadratic Surface

"旋转楼梯"面是直纹曲面,但它不是柱面,也不是二次曲面。《解析几何》二次曲面一章中有四个典型的直纹曲面即柱面、锥面、单叶双曲面、双曲抛物面,其中单叶双曲面、双曲抛物面的直纹性较难理解。文章认为,在正确理解概念的基础上,运用"析因式法",深入分析曲面方程的结构,掌握直母线方程,并借助理论推导和空间想象多角度、深层次地理解直母线的性质是掌握二次曲面直纹性的关键和学习要点。

＂Spiral staircase surface＂is a ruled surface. It is not cylindrical surface,is not quadratic surfaces. In the Chapter of Quadratic Surface of Analytic Geometry there are four typical straight line formed quadratic surfaces,i. e. cylindrical surface,cone,uniparted hperboloid,and hyperbolic paraboloid. Among them,the property of straight line formation for uniparted hperboloid and hyperbolic paraboloid is comparatively difficult to understand. The key to understanding and learning the property of straight line formation for quadratic surface is,based on a correct comprehension of the basic conceptions and a profound analysis of the structures of the quadratic surface formulas,to master the family formulas of the straight line,use theoretical deduction and spatial imagination,and perceive the property of the family of straight line from multi- angles and profound levels.