DOI: 10.3390/math11163495 ISSN:
Surface Pencil Pair Interpolating Bertrand Pair as Common Asymptotic Curves in Euclidean 3-Space
Fatemah Mofarreh, Rashad A. Abdel-Baky- General Mathematics
- Engineering (miscellaneous)
- Computer Science (miscellaneous)
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.