作为动直线运动轨迹的二次曲面  

Quadratic Surfaces Defined as Locus of Rectilinear Motion

作　　者：黄保军[1] 

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2016年第4期4-7,共4页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省高校省级教学质量与教学改革工程项目(2012gxk191)

摘　　要：二次曲面是空间解析几何最重要的内容之一.研究二次曲面,除利用平行截割法,通过综合分析截痕的变化来认识曲面的形状外,还可通过分析曲面的内部结构来把握其几何特征.文章基于单叶双曲面和双曲抛物面的直母线性质,详细论证了这2类曲面均是遵循一定规律的动直线的运动轨迹,从而直观揭示它们的几何特征,为利用几何法定义这些曲面奠定可靠的理论基础.Quadratic surfaces are important in solid analytic geometry. The shape of surfaces can be under-stood by using parallel section method and analyzing change of the sections. Geometric characteristics can al-so be understood by discussing internal structure of the surfaces. Based on the properties of the ruling of thesurfaces,we concluded that hyperboloid of one sheet and hyperbolic paraboloid are loci of rectilinear motioncomplying with some rules,which reveal their geometric characteristics. These results would be a theoreticalfoundation on defining the surfaces with the use of geometric method.

关 键 词：单叶双曲面 双曲抛物面 直母线 

分 类 号：O182.2[理学—数学]