THERMAL SCIENCE

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Tuba Ağirman Aydin

A SPECIAL INTERPRETATION OF THE CONCEPT CONSTANT BREADTH FOR A SPACE CURVE

ABSTRACT
The definition of curve of constant breadth in the literature is made by using tangent vectors, which are parallel and opposite directions, at opposite points of the curve. In this study, normal vectors of the curve, which are parallel and opposite directions are placed at the exit point of the concept of curve of constant breadth. And in this study, on the concept of curve of constant breadth according to normal vector is worked. At the conclusion of the study, is obtained a system of linear differential equations with variable coefficients characterizing space curves of constant breadth according to normal vector. The coefficients of this system of equations are functions depend on the curvature and torsion of the curve. Then is obtained an approximate solution of this system by using the Taylor matrix collocation method. In summary, in this study, a different interpretation is made for the concept of space curve of constant breadth, the first time. Then this interpretation is used to obtain a characterization. And as a result, this characterization we've obtained is solved.
KEYWORDS
constant breadth, Special curves in space, Taylor matrix collocation method
PAPER SUBMITTED: 2018-11-15
PAPER REVISED: 2018-12-20
PAPER ACCEPTED: 2019-01-05
PUBLISHED ONLINE: 2019-03-09
DOI REFERENCE: https://doi.org/10.2298/TSCI181115050A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S371 - S382]
REFERENCES
  1. Euler, L., De Curvis trangularibis, Acta Academiae Petropol, (1778, 1780), 3-30
  2. Reuleaux, F., The Kinematics of Machinery, Trans. By Kennedy A.B.W., Dover Pub., New York, 1963
  3. Fujivara, M., On Space Curves of Constant Breadth, Thoku Math Journal, 5 (1914), pp. 179-184
  4. Akdoğan, Z., Mağden, A., Some Characterization of Curves of Constant Breadth in En Space, Turkish Journal of Mathematics, 25 (2001), pp. 433-444
  5. Altunkaya, B., Aksoyak, F.K., Null Curves of Constant Breadth in Minkowski 4-Space, Communications Faculty Science University Ankara Series A1: Mathematics and Statistics, 68 (2018), 1, pp. 451-456
  6. Mağden, A., Köse, Ö., On the Curves of Constant Breadth in E4 Space, Turkish Journal of Mathematics, 21 (1997), pp. 277-284
  7. Önder, M., et al., Differential Equations Characterizing Timelike and Spacelike Curves of Constant Breadth in Minkowski 3-Space E13, Journal of the Korean Mathematical Society 48 (2011), 4, pp. 849-866
  8. Yılmaz, S., Turgut, M., Partially Null Curves of Constant Breadth in Semi-Riemannian Space, Modern Applied Science, 3 (2009), 3, pp. 60-63
  9. Mellish, A.P., Notes on Differential Geometry, Annals of Mathematics 32 (1931), 1, pp. 181-190
  10. Sezer, M., Integral Characterizations for A System of Frenet Like Differential Equations and Applications, Proceeding (E. U. Faculity of Science, Series Of Scientific Meetings), Vol 1, 1991, pp. 435-444
  11. Dannon, V., Integral Characterizations and the Theory of Curves, Proceedings of the American Mathematical Society, 81 (1981), 4, pp. 600-602
  12. Sezer, M., Differential Equations Characterizing Space Curves of Constant Breadth and A Criterion for These Curves, Doğa TU J. Math., 13 (1989), 2, pp. 70-78
  13. Hacısalihoğlu, H.H., Diferensiyel Geometri (Differential Geometry), Ankara Uni. Faculty of Science, Ankara, 1993
  14. Köse, Ö., On Space Curve of Constant Breadth, Doğa TU Journal Mathematics, 10 (1986), 1, pp. 1-14
  15. Walrave, J., Curves and Surfaces in Minkowski Space, Ph. D. Thesis, K. U. Leuven, Faculty of Sciences, Leuven, 1995
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A special interpretation of the concept constant breadth for a space curve

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence