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2017•DergiPark (Istanbul University)Requires access

ON DEVELOPABLE RULED SURFACE OF THE PRINCIPAL-DIRECTION CURVE

Beyhan Yılmaz, Çağla Ramis, Yusuf Yaylı

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Abstract

This study is devoted to improve the theory of the developable ruled surfaces in terms of principal-direction curves of any spatial curve in three-dimensional Euclidean space. We obtain the new representation for developable surfaces by slant helices and the useful elements such as pitch, angle of pitch and dral with the help of a new frame $\\left \\{ N,C,W\\right \\} $. Furthermore, the investigation is observed under some special cases in terms of the director vector of surface.

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What this paper is about

This study is devoted to improve the theory of the developable ruled surfaces in terms of principal-direction curves of any spatial curve in three-dimensional Euclidean space. We obtain the new representation for developable surfaces by slant helices and the useful elements such as pitch, angle of pitch and dral with the help of a new frame $\\left \\{ N,C,W\\right \\} $. Furthermore, the investigation is observed under some special cases in terms of the director vector of surface.

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Available abstract

This study is devoted to improve the theory of the developable ruled surfaces in terms of principal-direction curves of any spatial curve in three-dimensional Euclidean space. We obtain the new representation for developable surfaces by slant helices and the useful elements such as pitch, angle of pitch and dral with the help of a new frame $\\left \\{ N,C,W\\right \\} $. Furthermore, the investigation is observed under some special cases in terms of the director vector of surface.

Key concepts: Developable surface, Ruled surface, Geometry, Surface (topology), Mathematics, Space (punctuation), Representation (politics), Euclidean geometry

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