ASPECTS AND GEOMETRIC INTERPRETATION IN SOLVING CONICAL SECTIONS

Alina Duta; Ionut - Daniel Geonea; Gordana Djukanovic; Marcela Popescu; Ludmila Sass

Authors

Alina Duta Ph.D. Eng. University of Craiova
Ionut - Daniel Geonea Ph.D. Eng. University of Craiova https://orcid.org/0000-0001-8844-0497
Gordana Djukanovic Ph.D. Eng. University of Belgrade
Marcela Popescu Ph.D. Eng. University of Craiova
Ludmila Sass Ph.D. Eng. 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.

Downloads

Download data is not yet available.

Author Biographies

Alina Duta Ph.D. Eng., University of Craiova

Associate Professor Faculty of Mechanics

Ionut - Daniel Geonea Ph.D. Eng., University of Craiova

Associate Professor Faculty of Mechanics

Gordana Djukanovic Ph.D. Eng., University of Belgrade

Assistant Professor Faculty of Forestry

Marcela Popescu Ph.D. Eng., University of Craiova

Associate Professor Faculty of Science Department of Applied Mathematics

Ludmila Sass Ph.D. Eng., University of Craiova

Associate Professor Faculty of Mechanics

References

https://en.wikipedia.org/wiki/Apollonius_of_Perga, Accessed: 2019-01-15

Ionescu, Gh.D. (1984). Teoria diferentiala a curbelor si suprafetelor cu aplicatii tehnice. Editura Dacia, Cluj-Napoca.

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.

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