曲线按其从可展曲面分类

CURVES CLASSIFIED BY THEIR RECTIFYING DEVELOPABLE

本文利用微分几何的方法给出了一种曲线的分类法。将非直线的曲线按其从可展曲面分为柱面曲线、锥面曲线和切线面曲线三大类,并证明了这三类曲线的曲率及挠率特征。讨论了Bertrand曲线与广义螺线的分类问题,提出了Bertrand曲线与柱面螺线的又一充要条件,并进一步讨论了切线面曲线及其对应曲线问题。

This article gives a taxonomy of Curves by the Way of differential geometry According to the rectifying developable Curves of non - line may Consist of Cylindrical curve,conical Curve and tangent Surface Curve.This proves that these three kinds of curves are characterized as curvature and torsion This article also gives a discussion of the taxonomy of Bertrand curve and generalized helix [2] and gives another necessary and sufficient condition of Bertrand curve and Cylindrical helix.It further discusses the Problem of tangent surface curve and its Corresponding curve.