ASPECTS AND GEOMETRIC INTERPRETATION IN SOLVING CONICAL SECTIONS

  • Alina DUTA University of Craiova
  • Ionut - Daniel GEONEA University of Craiova
  • Gordana DJUKANOVIC University of Belgrade
  • Marcela POPESCU University of Craiova
  • Ludmila SASS University of Craiova
Keywords: conic, sections, decomposition, inclined surface, ellipse, parabola, hyperbola

Abstract

In mathematics, a conic is the curve that is obtained by intersecting a plane with a cone. Is well known that the shape of this curve may differ quite a bit depending on the position of the intersection plane relative to the cone axis, as it is actually a family of curves, commonly called "conical". In the first part, we determine the relation between the shape of the section curve and the angle of the plane of the section plane. The paper also proposes a reassembly of the cone from the fragments resulting from the sectioning with different planes. These recommences can be found as technical solutions for joining two pipes with different diameters and whose axes are not coaxial.

Author Biographies

Alina DUTA, University of Craiova

University of Craiova, Faculty of Mechanics.

Ionut - Daniel GEONEA, University of Craiova

University of Craiova, Faculty of Mechanics.

Gordana DJUKANOVIC, University of Belgrade

Faculty of Forestry, University of Belgrade, SERBIA.

Marcela POPESCU, University of Craiova

Department of Applied Mathematics, Faculty of Science.

Ludmila SASS, University of Craiova

University of Craiova, Faculty of Mechanics.

References

1 https://en.wikipedia.org/wiki/Apollonius_of_Perga, Accessed: 2019-01-15
2 Ionescu, Gh.D. (1984). Teoria diferentiala a curbelor si suprafetelor cu aplicatii tehnice. Editura Dacia, Cluj-Napoca.
3 Sass, L., Duta, A., Popa, D.L. (2014) Computer Aided Graphics / Grafica asistata de calculator, ed. a II-a, Editura SITECH, ISBN 978-606-11-3940-8, Craiova.
4 Xu Yaqi, ZhangChengfang, Mi Xinwu (2018) Geometric Analysis and Engineering Application of Conic Section, ICGG2018 – Proceedings of the 18th International Conference on Geometry and Graphics, Advanced in Intelligent Systems and Computing809, pp. 2274-2281, Springer International Publishing AG, https://doi.org./10.1007/978-3-95588-9_219
Published
2019-05-10
How to Cite
DUTA, A., GEONEA, I.- D., DJUKANOVIC, G., POPESCU, M., & SASS, L. (2019). ASPECTS AND GEOMETRIC INTERPRETATION IN SOLVING CONICAL SECTIONS. Journal of Industrial Design and Engineering Graphics, 14(1), 23-26. Retrieved from http://sorging.ro/jideg/index.php/jid/article/view/419
Section
Articles