Abstract
Matematikçiler yüzyıllardır yüzeyler teorisini araştırmışlardır. Bu çalışmada, üç boyutlu Öklid uzayı E^3'de strophoidal yüzeyi ele aldık. Öklid geometrisinin notasyonlarını sunduk. İlave olarak, bir helisoidal yüzeyi vererek, strophoidal yüzeyi tanımladık ve Gauss tasvirini, Gauss eğriliğini, ortalama eğriliğini hesapladık. Son olarak, bu tür yüzeylerin ortalama eğriliği ve Gauss eğriliği ile ilgili bazı bağıntıları verdik.
References
- L.P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces. Dover Publications, N.Y. 1909.
- A.R. Forsyth, Lectures on the Differential Geometry of Curves and Surfaces. Cambridge Un. press, 2nd ed. 1920.
- A. Gray, S. Salamon, and E. Abbena, Modern Differential Geometry of Curves and Surfaces with Mathematica. Third ed. Chapman & Hall/CRC Press, Boca Raton, 2006.
- H.H. Hacısalihoğlu, Diferensiyel Geometri I. Ankara Ün., Ankara, 1982.
- H.H. Hacısalihoğlu, 2 ve 3 Boyutlu Uzaylarda Analitik Geometri. Ertem Basım, Ankara, 2013.
- J.C.C. Nitsche, Lectures on Minimal Surfaces, Introduction, Fundamentals, Geometry and Basic Boundary Value Problems. Cambridge University Press, Cambridge, 1989.
- M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. IV. Third edition. Publish or Perish, Inc., Houston, Texas, 1999.
Abstract
The mathematicians for centuries have researched the surfaces theory. In this paper, we consider strophoidal surface in three dimensional Euclidean space E^3. We present notations of a Euclidean geometry. In addition, stating a helicoidal surface, we define strophoidal surface, and calculate its Gauss map, Gaussian curvature, mean curvature. Finally, we give some relations of the Gaussian curvature and the mean curvature of that kind surfaces.
References
- L.P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces. Dover Publications, N.Y. 1909.
- A.R. Forsyth, Lectures on the Differential Geometry of Curves and Surfaces. Cambridge Un. press, 2nd ed. 1920.
- A. Gray, S. Salamon, and E. Abbena, Modern Differential Geometry of Curves and Surfaces with Mathematica. Third ed. Chapman & Hall/CRC Press, Boca Raton, 2006.
- H.H. Hacısalihoğlu, Diferensiyel Geometri I. Ankara Ün., Ankara, 1982.
- H.H. Hacısalihoğlu, 2 ve 3 Boyutlu Uzaylarda Analitik Geometri. Ertem Basım, Ankara, 2013.
- J.C.C. Nitsche, Lectures on Minimal Surfaces, Introduction, Fundamentals, Geometry and Basic Boundary Value Problems. Cambridge University Press, Cambridge, 1989.
- M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. IV. Third edition. Publish or Perish, Inc., Houston, Texas, 1999.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | March 31, 2022 |
| Published in Issue | Year 2022 |