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Journals / Turkish Journal of Mathematics and Computer Science / 2021 / Cilt: 13 - Sayı: 1

Quaternionic and Dual Quaternionic Darboux Ruled Surfaces

Abdussamet Calışkan
Pages
106–114
Publication Date
2022-11-02
DOI
—
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AI Summary & Key Takeaways

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

Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of dual spatial quaternions and dual integral invariants of the ruled surface are obtained.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, firstly the ruled surface drawn by the Darboux vector is expressed as a quaternion.
📊
Key Findings & Data:Then, the spatial quaternionic definition of the striction curve is given and the integral invariants of the surface are calculated.
💡
Conclusion & Impact:Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of dual spatial quaternions and dual integral invariants of the ruled surface are obtained.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, firstly the ruled surface drawn by the Darboux vector is expressed as a quaternion. Then, the spatial quaternionic definition of the striction curve is given and the integral invariants of the surface are calculated. Finally, the ruled surface which corresponds to a dual curve drawn by a dual Darboux vector is derived with the help of dual spatial quaternions and dual integral invariants of the ruled surface are obtained.

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Cite This Article

Calışkan, A. (2022). Quaternionic and Dual Quaternionic Darboux Ruled Surfaces. Turkish Journal of Mathematics and Computer Science, Cilt: 13 - Sayı: 1, 106–114. https://ajindex.com/articles/609067

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