On the Blaschke approach of ruled surface
Rashad A. Abdel-Baky
Abstract
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Rashad A. Abdel-Baky
Abstract
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In this paper using E. Study map and the Blaschke approach we studied a ruled surface as a curve on the dual unit sphere. The Blaschke approach proceeds by defining a sequence of ruled surfaces associated with the ruled surface. The relative positions of these surfaces and their distribution parameters characterize the local properties of the original surface. A necessary condition for a ruled surface to be closed is derived. Moreover, an example of application is investigated in detail.
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In this paper using E. Study map and the Blaschke approach we studied a ruled surface as a curve on the dual unit sphere. The Blaschke approach proceeds by defining a sequence of ruled surfaces associated with the ruled surface. The relative positions of these surfaces and their distribution parameters characterize the local properties of the original surface. A necessary condition for a ruled surface to be closed is derived. Moreover, an example of application is investigated in detail.
Key concepts: Ruled surface, Surface (topology), Mathematics, Blaschke product, Sequence (biology), Unit (ring theory), Dual (grammatical number), Geometry