有关法曲率的若干性质

Several Tinding about Normal Cuvarture

以[2]中经典微分几何问题为切入点,运用复数与三角工具广泛深入地探讨了“过曲面上一点有n条切线,若相邻两条切线的交角为2nπ,曲面法线与切线所定平面截得曲线的曲率半径为ρ1,ρ2,ρ3,…,ρn时,∑ni=11ρim,∑ni=1ρi,∏ni=1ρi的结果”,得到了法曲率与相关的三个有趣定理.

In this article which beginning with the problems of classical differential geometry in book [2]. The author probes into the problem related with normal curvature by using the knowledge of complex number and trigonometry. Among the n tangent lines through one pornt on the curve surface, if the angle of insection of two consecutive lines is 2π/n, n and the radius of curvature of the curve which are cut from the curve surface by the plane decided by the normal lines and tangent lines of the curve surface at the point are ρ1 ,ρ2 ,ρ3, … ,ρn respectively, three interesting theorems related with normal curvature will be get by ealeularing ∑i=1^n1/ρi^m,∑i=1^nρi,Пi=1^nρi.