单叶双曲面轨迹问题的相关研究

Research on the Trajectory of Hyperboloid of One Sheet

从一道全国大学生数学竞赛试题出发,研究了单叶双曲面可看成异面直线上动点满足一定条件的运动轨迹问题,并从微分几何的角度推导出单叶双曲面上特殊截面和截线方程,以验证其直纹性,同时还得到单叶双曲面单参数的直母线族方程,并直观地揭示了直母线的几何特征.

In accordance with National Mathematics Contest for College Students,the trajectory is studied which came from a point of non-coplanar straight line in space meet certain conditions.We deduced a special section line of the hyperboloid of one sheet which agrees with the definition of differential geometry and analyzed its property of ruled surface.On the other hand,we concluded the rectilinear generator of a hyperboloid of one sheet with single parameter which reveals their geometric characteristics.