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Journals / Teknik Bilimler Dergisi / 2018 / Cilt: 8 - Sayı: 2

Direction curves of principal normal indicatrix of a curve

Bir eğrinin asli normaller göstergesinin doğrultu eğrileri

Burak ŞAHİNER
Pages
46–54
Publication Date
2018-07-30
DOI
—
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AI Summary & Key Takeaways

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

Finally, a related example is given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Helices and slant helices are curves which are often encountered in nature and science and have a wide range of uses including computer aided geometric design, fractal geometry, kinematics, and DNA double.
📊
Key Findings & Data:In this paper, direction curves of principal normal indicatrix of a curve in Euclidean 3-space are defined and some relationships between Frenet vectors and curvatures of these curves are found.
💡
Conclusion & Impact:Finally, a related example is given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Doğrultu eğrileri · helis · küresel helis

Abstract

Helices and slant helices are curves which are often encountered in nature and science and have a wide range of uses including computer aided geometric design, fractal geometry, kinematics, and DNA double. In this paper, direction curves of principal normal indicatrix of a curve in Euclidean 3-space are defined and some relationships between Frenet vectors and curvatures of these curves are found. By using these direction curves, some useful methods to construct helices and slant helices from spherical curves are obtained. Finally, a related example is given.

Özet

Helisler ve slant helisler, doğada ve bilimde sıklıkla karşılaştığımız, bilgisayar destekli geometrik tasarımdan fraktal geometriye, kinematikten DNA çiftlerine, geniş bir kullanım alanına sahip olan eğrilerdir. Bu çalışmada, 3-boyutlu Öklid uzayında bir eğrinin asli normaller göstergesinin doğrultu eğrileri tanımlanmış ve bu eğrilerin Frenet vektörleri ve eğrilikleri arasındaki ilişkiler bulunmuştur. Bu doğrultu eğrileri kullanılarak, küresel eğrilerden helis ve slant helisler oluşturmak için kullanışlı yöntemler elde edilmiştir. Son olarak, konu ile ilgili bir örnek verilmiştir.

🔖

Cite This Article

ŞAHİNER, B. (2018). Direction curves of principal normal indicatrix of a curve. Teknik Bilimler Dergisi, Cilt: 8 - Sayı: 2, 46–54. https://ajindex.com/articles/805694

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References (11)

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