关于封闭曲线的切线象

ON THE TANGENT SPHERICAL IMAGE OF A CLOSED SPACE CURVE

W.Fenchel曾证明,封闭空间曲线的切线象的长不小于2π。本文证明的下列定理是Fenchel定理的推广,定理,议c’是空间封闭曲线c的切线象,则必存在一个内接于c’的球面内接n边形p(n≤5),p的长不小于2π。

W. Fenchel proved that the length of the tangent spherical image of a closed space curve is at least 2π. In this paper, we prove the following theorem. It is a generalization of Fenchel's theorem.Theorem. It c is the tangent spherical image of a closed space curve c, then there is a spherical n-polygon (n≤5) p inscribed in c' and the length of p is at least 2π.