A New Type of Helix Constructed by Plane Curves

Abstract

Abstract. In this paper, we give an algorithm to construct a space curve in Euclidean 3-space E 3 from a plane curve which is called PDP-helix of order d. The notion of the PDP-helices is a generalization of a general helix and a slant helix in E 3 . It is naturallyshown that the PDP-helix of order 1 and order 2 are the same as the general helix and the slant helix, respectively. We give a characterization of the PDP-helix of order d. Moreover, we study some geometric properties of that of order 3.