Surface Pencil Pair Interpolating Bertrand Pair as Common Asymptotic Curves in Euclidean 3-Space

Fatemah Mofarreh () and Rashad A. Abdel-Baky ()
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Fatemah Mofarreh: Mathematical Science Department, Faculty of Sciences, Princess Nourah bint Abdulrahman, Riyadh 11546, Saudi Arabia
Rashad A. Abdel-Baky: Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt

Mathematics, 2023, vol. 11, issue 16, 1-12

Abstract: In this paper, we obtain the necessary and sufficient conditions of a surface pencil pair interpolating a Bertrand pair as common asymptotic curves in Euclidean 3-space E 3 . Afterwards, the conclusion to the ruled surface pencil pair is also obtained. Meanwhile, the epitomes are stated to emphasize that the proposed methods are effective in product manufacturing by adjusting the shapes of the surface pencil pair.

Keywords: asymptotic curve; Bertrand mate; ruled surface (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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