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Journals / International Electronic Journal of Geometry / 2026 / Volume: 19 Issue: 2

New Special Curves Using a Pair of Orthogonal Curves.

Ahmad Ali(King Abdulaziz University)0000-0003-3747-4990
Lamia Saeed Alqahtani(King Abdulaziz University)0000-0002-6137-1505
Batool Althaqafi(King Abdulaziz University)0009-0002-2796-9447
Pages
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Publication Date
2026-10-25
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Several illustrative examples are presented, for which both the intrinsic equations and the corresponding parametric representations are obtained and graphically visualized.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce a new family of special curves in Euclidean 3-space, called the generalized k−slant helix, which extends the classical notion of the k−slant helix.
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Key Findings & Data:A particular subclass of this family, referred to as the generalized k−slant helix of type NB (denoted by G-k-SH-NB), is studied in detail.
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Conclusion & Impact:Several illustrative examples are presented, for which both the intrinsic equations and the corresponding parametric representations are obtained and graphically visualized.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:General helix · slant helix · slant-slant helix

Abstract

In this paper, we introduce a new family of special curves in Euclidean 3-space, called the generalized k−slant helix, which extends the classical notion of the k−slant helix. A particular subclass of this family, referred to as the generalized k−slant helix of type NB (denoted by G-k-SH-NB), is studied in detail. By employing a pair of orthogonal associated curves, we derive the intrinsic equations of this class of curves and obtain the parametric representation of their position vectors with respect to the arc-length parameter. Furthermore, starting from a general helix, we apply this approach to determine the parametric representation of the G-k-SH-NB in terms of the arc-length parameter. Several illustrative examples are presented, for which both the intrinsic equations and the corresponding parametric representations are obtained and graphically visualized.

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Cite This Article

Ali, A., Alqahtani, L. S., Althaqafi, B. (2026). New Special Curves Using a Pair of Orthogonal Curves.. International Electronic Journal of Geometry, Volume: 19 Issue: 2. https://doi.org/10.36890/iejg.1937634

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