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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 17 Sayı: 2

A Generalization of Curve Mates: Normal Mate of a Curve

Oğuzhan Çelik(PAMUKKALE UNIVERSITY, BEKİLLİ VOCATIONAL SCHOOL)0000-0001-5331-5100
Pages
338–352
Publication Date
2024-08-31
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AI Summary & Key Takeaways

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

In the conclusion, it is expressed express which famous pairs of curves will be obtained in which particular case.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This a paper, a new curve pair is defined that generalizes some pairs of curves well known as Mannheim and Bertrand curve pairs.
📊
Key Findings & Data:A normal curve pair is defined in such a way that a vector u obtained by overlapping the normal planes of the G and G* curves makes the same angle as the binormals of these curves.
💡
Conclusion & Impact:In the conclusion, it is expressed express which famous pairs of curves will be obtained in which particular case.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Normal mate · Curve mates · Mannheim mate

Abstract

This a paper, a new curve pair is defined that generalizes some pairs of curves well known as Mannheim and Bertrand curve pairs. A normal curve pair is defined in such a way that a vector u obtained by overlapping the normal planes of the G and G* curves makes the same angle as the binormals of these curves. The relationship between torsions and curvatures of curve pairs was analyzed. Moreover, The unit quaternion q corresponding to the rotation matrix between the Frenet vectors of the curves was defined. In the conclusion, it is expressed express which famous pairs of curves will be obtained in which particular case.

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Cite This Article

Çelik, O. (2024). A Generalization of Curve Mates: Normal Mate of a Curve. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 17 Sayı: 2, 338–352. https://doi.org/10.18185/erzifbed.1396745

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