King Abdul Aziz University, Faculty of Science, Department of Mathematics, P.O. Box 80203, Jeddah 21589, Saudi Arabia Al-Azhar University, Faculty of Science, Mathematics Department, Nasr City, 11884 Cairo, Egypt
10.1016/j.joems.2011.12.005
Abstract
In this paper, position vector of a slant helix with respect to standard frame in Euclidean space E3 is studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine a position vector of an arbitrary slant helix. In terms of solution, we determine the parametric representation of the slant helices from the intrinsic equations. Thereafter, we apply this method to find the parametric representation of a Salkowski curve, anti-Salkowski curve and a curve of constant precession, as examples of a slant helices, by means of intrinsic equations.
Ali, A. T. (2024). Position vectors of slant helices in Euclidean 3-space. Journal of the Egyptian Mathematical Society, 20(1), 1-6. doi: 10.1016/j.joems.2011.12.005
MLA
Ahmad T. Ali. "Position vectors of slant helices in Euclidean 3-space", Journal of the Egyptian Mathematical Society, 20, 1, 2024, 1-6. doi: 10.1016/j.joems.2011.12.005
HARVARD
Ali, A. T. (2024). 'Position vectors of slant helices in Euclidean 3-space', Journal of the Egyptian Mathematical Society, 20(1), pp. 1-6. doi: 10.1016/j.joems.2011.12.005
VANCOUVER
Ali, A. T. Position vectors of slant helices in Euclidean 3-space. Journal of the Egyptian Mathematical Society, 2024; 20(1): 1-6. doi: 10.1016/j.joems.2011.12.005
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