A New Type of Helix Constructed by Plane Curves
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In this paper, we give an algorithm to construct a space curve in Euclidean 3-space $\mathbb{E}^3$ 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 $\mathbb{E}^3$. It is naturally shown 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.
Abstract
In this paper, we give an algorithm to construct a space curve in Euclidean 3-space $\mathbb{E}^3$ 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 $\mathbb{E}^3$. It is naturally shown 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.
참고문헌 (6)
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