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

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

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 E3. Afterwards, the conclusion to the ruled surface pencil pair is also obtained. Meanwhile, the epitomes are stated to emphasize t...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 11; no. 16; p. 3495
Main Authors: Mofarreh, Fatemah, Abdel-Baky, Rashad A.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01-08-2023
Subjects:
Analysis
Asymptotes
asymptotic curve
Asymptotic properties
Bertrand mate
Curves
Euclidean geometry
Euclidean space
Geometry, Plane
Geometry, Solid
Interpolation
Mathematics
Methods
ruled surface
Trends
Saudi Arabia
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Summary: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 E3. 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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11163495