CURVATURE PROPERTIES AND PLANE CURVES

Kamoliddinov Davlatjon Utkirkhon o‘g‘li.

doi:10.1808/ya61hw96

Авторы

Kamoliddinov Davlatjon Utkirkhon o‘g‘li. Master’s degree student Samarkand state university named after Sharof Rashidov Автор

DOI:

https://doi.org/10.1808/ya61hw96

Ключевые слова:

Regular curves, tractrix, smooth function, plane curvature, tangent vector, normal vector, binormal vector.

Аннотация

In this article, we will study many properties and characteristics of curves.In addition, we will reveal their important aspects through the tangent vector,the normal vector and the binormal vector.At the end of the article, we will provide the proof of an important theorem related to the theory of curves.Moreover, the essence of the article is revealed by citing specific examples.

Библиографические ссылки

Kreyszig Erwin, Differential Geometry, Leizpig, 1957.

L.P. Eisenhart. An Introduction to Differential Geometry, Princeton, 1940.

Kristopher Tapp. Differential Geometry of curves and surfaces, Switzerland, 2016.

Pavel Tumarkin. Differential geometry lectures, Durham University, 2016.

S. Sawin. An Invitation to Differential Geometry, 2015.

B–Y. Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer. Math. Monthly 110 (2003) 147–152.

B–Y. Chen and F. Dillen, Rectifying curves as centrodes and extremal curves, Bull. Inst. Math. Academia Sinica 33 (2) (2005)77–90 .

F. F. Chen, Introduction to Plasma Physics, Springer, New York 1974.

S. Deshmukh, B–Y. Chen, and S. H. Alshammari, On rectifying curves in Euclidean 3–space, Turk. J. Math., 42 (2018) 609–620.

R. T. Farouki, Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable, Springer, Berlin 2008.

R. T. Farouki, C. Giannelli, and A. Sestini, Helical polynomial curves and double Pythagorean hodographs I. Quaternion and Hopf map representations, J. Symb. Comput. 44 (2) (2009) 161–179.

R. T. Farouki, C. Giannelli, and A. Sestini, Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves, J. Symb. Comput. 44 (2009) 307–332.

R. T. Farouki, C. Y. Han, C. Manni, and A. Sestini, Characterization and construction of helical polynomial space curves, J. Comput. Appl. Math. 162 (2004) 365–392.

R. T. Farouki and T. Sakkalis, Rational space curves are not “unit speed,” Comput. Aided Geom. Design 24 (2007) 238–240.

Zafarjon o‘g‘li, Muydinov Muhammadzoir. "SHOYIM BO ‘TAYEV HIKOYALARIDA XARAKTERLAR TASVIRI." Konferensiyalar| Conferences. Vol. 1. No. 4. 2024.

Zafarjon o'g'li, Muydinov Muhammadzoir. "ANVAR OBIDJON ASARLARINING NASRIY POETIKASI." (2023).

Zafarjon o'g'li, Muydinov Muhammadzoir. "ANVAR OBIDJONNING IJOD LABARATORIYASINING SHAKLLANISHIGA BIR NAZAR." (2023).