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Journals / Konuralp Journal of Mathematics / 2026 / Volume: 4 Issue: 1

SOME CHARACTERIZATIONS OF EULER SPIRALS IN E3

Semra Saracoglu Çelik
Yusuf Yaylı
Erhan Güler
Pages
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Publication Date
2016-04-01
DOI
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AI Summary & Key Takeaways

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

The approach we used in this paper is useful in understanding the role of Euler spirals in E3 1 in di erential geometry.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, some characterizations of Euler spirals in E3 1 have been presented by using their main property that their curvatures are linear.
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Key Findings & Data:Moreover, discussing some properties of Bertrand curves and helices, the relationship between these special curves in E3 1 have been investigated with di erent theorems and examples.
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Conclusion & Impact:The approach we used in this paper is useful in understanding the role of Euler spirals in E3 1 in di erential geometry.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Curvature · Cornu spiral · Bertrand curve pair

Abstract

In this study, some characterizations of Euler spirals in E3 1 have been presented by using their main property that their curvatures are linear. Moreover, discussing some properties of Bertrand curves and helices, the relationship between these special curves in E3 1 have been investigated with di erent theorems and examples. The approach we used in this paper is useful in understanding the role of Euler spirals in E3 1 in di erential geometry.

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Cite This Article

Çelik, S. S., Yaylı, Y., Güler, E. (2016). SOME CHARACTERIZATIONS OF EULER SPIRALS IN E3. Konuralp Journal of Mathematics, Volume: 4 Issue: 1. https://ajindex.com/articles/1521920

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References (7)

  1. Harary, G., Tal, A., 3D Euler Spirals for 3D Curve Completion, Symposium on Computational Geometry 2010: 107-108.
  2. Harary, G., Tal, A., The Natural 3D Spiral, Computer Graphics Forum, Volume 30(2011), Number 2: 237-246.
  3. Kalkan, B., Lopez, R., Spacelike surfaces in Minkowski space satisfying a linear relation between their principal curvatures, Di erential Geometry-Dynamical Systems, Vol.13, 2011, pp. 107-116.
  4. K. Ilarslan, E. Nesovic, and M. Petrovic-Torgasev, Some Characterizations of Rectifying Curves in the Minkowski 3-space, Novi Sad J. Math. 33 (2003), no. 2, 23f32g.
  5. Lopez, R., Di erential Geometry of Curves and Surfaces in Lorentz-Minkowski Space. [arXiv:0810.3351v1] math.DG, 2008.
  6. Saracoglu Celik, S., Yayli, Y., Guler, E., On Generalized Euler Spirals in E3, International Journal of Geometry (Accepted).
  7. http://www.cs.iastate.edu/~cs577/handouts/curvature.pdf.