2015 # On the Differential Geometric Elements of the Involute $${\tilde{\rm D}}$$ D ~ -Scroll in E 3

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“…In this section we will define and work on MDRS, which is known as rectifying developable ruled surface, orD scroll as in [7] where the differential geometric elements of the involuteD − scroll.are examined too. Here first we will give Darboux vector field of the Mannheim partner α * as in the following theorem.…”

confidence: 99%

“…In this section we will define and work on MDRS, which is known as rectifying developable ruled surface, orD scroll as in [7] where the differential geometric elements of the involuteD − scroll.are examined too. Here first we will give Darboux vector field of the Mannheim partner α * as in the following theorem.…”

confidence: 99%

“…Proof. Since the normal vector field N of DR α is [7], and the normal vector field N * of MDRS of the curve α is…”

confidence: 99%

“…He also defined the equation for an enveloping curve of the family of normal planes for a space curve. Suleyman and Seyda [3] determined the concept of parallel curves, which means that if the evolute exists, then the evolute of the parallel arc will also exist and the involute will coincide with the evolute. Brewster and David [4] stated that a curve is composed of two arcs with a common evolute, and the common evolute of two arcs must be a curve with only one tangent in each direction.…”

confidence: 99%

“…By using the similiar method we produce a new ruled surface based on the other ruled surface. The differential geometric elements of the involuteD scroll are examined in [9]. It is well-known that, if a curve is differentiable in an open interval, at each point, a set of mutually orthogonal unit vectors can be constructed.…”

confidence: 99%