journal6 ›› 2007, Vol. 28 ›› Issue (3): 10-11.

• Mathematics • Previous Articles     Next Articles

Developable Surfaces Generated by a Directrix


  1. (College of Mathematics and Copmuter Science,Jishou University,Jishou 416000,Hunan,China)
  • Online:2007-05-25 Published:2012-08-27

Abstract: In this paper we discuss how to obtain  a developable surface from some families of straight along a curve.The main results are:(1) The ruled surface generate by a directrix Γ:r=r(s)  and the rulings α(s)cos θ(s)+γ(s)sin θ(s) is developable if and only if tan θ(s)=k(s)/τ(s),where α and γ are the unit tanqent vectors and binormal vectors of Γ respectively,k and τ are curvature and torsion functions of Γ respectively;(2) Let Γ be a curve on the surface S,then the  ruled surface can be generated by the directrix Γ and the rulings ε(s)cos θ(s)+n(s)sin θ(s)  is developable if and only if θ(s)=∫ss0τg(s)ds+θ0,where n(s) is the normal vector of S at s,ε=n×α,τg is the gesdesic torsion of S along Γ.

Key words: development surface, curve, family of straight lines

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