正螺面上的圆柱螺线  

Circular Helices on a Helicoid

作　　者：陶雅 张量 TAO Ya;ZHANG Liang(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241000)

机构地区：[1]安徽师范大学数学与统计学院,芜湖241000

出　　处：《高等数学研究》2024年第1期33-36,107,共5页Studies in College Mathematics

基　　金：安徽师范大学本科生优秀毕业论文(设计、创作)培育计划项目(pyjh2020252).

摘　　要：本文主要证明了正螺面上与其同轴方向的一般螺线必为圆柱螺线,确定了正螺面上所有圆柱螺线的参数表示.此外,通过示例说明了正螺面与圆柱面交线为圆柱螺线的条件.In this paper,we prove that the general helix on a helicoid with the same axis direction must be a circular helix,and we determine the parametrization of all circular helices with the same axis direction on a helicoid.In addition,the condition that the intersection of the helicoid and the cylinder is a circular helix is illustrated by examples.

关 键 词：正螺面 圆柱螺线 圆柱面 

分 类 号：O186.11[理学—数学]