单叶双曲面与双曲抛物面为动直线轨迹的定义  

Hyperboloid of One Sheet and Hyperbolic Paraboloid Defined as Locus of Moving Strait-Lines

作　　者：陈岱婉 陈彦 CHEN Daiwan;CHEN Yan(Shantou Preschool Education College,Shantou 515041,Guangdong,China)

机构地区：[1]广东汕头幼儿师范高等专科学校初等教育学院,广东汕头515041

出　　处：《汕头大学学报（自然科学版）》2023年第3期25-32,共8页Journal of Shantou University：Natural Science Edition

基　　金：2020年广东省科技专项资金(“大任务+任务清单”)资助科研项目(200111165873103);广东汕头幼儿师范高等专科学校2022年科研课题(STYGZ-2022-JYZX11)。

摘　　要：单叶双曲面与双曲抛物面作为一类重要的直纹面,到目前尚无直线轨迹的定义.本文从二次曲面的内在关联出发,借鉴柱面和锥面的定义,分别利用渐近锥面或一对相交平面作为辅助曲面,找到生成这两种直纹面各自的准线及其对应的动直线,进而给出这两种直纹面为动直线轨迹的定义,使其直纹性更直观,也充分体现了其几何特征.Hyperboloid of one sheet and hyperbolic paraboloid are special rectilinear surfaces.Definition is not found for locus of the moving strait-lines.Under the inherent relevance among quadratic surfaces,following the definitions of a cylinder and a cone and utilizing an asymptotic cone or a pair of intersecting planes,respectively,as anauxiliary figure,the directrixes and its corresponding moving strait-lines generating hyperboloid of one sheet and hyperbolic paraboloid are shown.Finally,an intuitive definition is given that both rectilinear surfaces are defined as locus of moving strait-lines,and the geometrical characters are also represented.

关 键 词：单叶双曲面 双曲抛物面 动直线 轨迹 

分 类 号：O182.2[理学—数学]