Original scientific paper

On the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space

Géza Csima ; Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary
Jenő Szirmai orcid.org/0000-0001-9610-7993 ; Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary

Abstract

The theory of the isoptic curves is widely studied in the Euclidean plane E^2 (see [1] and [13] and the references given there). The analogous question was investigated by the authors in the hyperbolic H^2 and elliptic E^2 planes (see [3], [4]), but in the higher dimensional spaces there is no result according to this topic.
In this paper we give a natural extension of the notion
of the isoptic curves to the n-dimensional Euclidean space E^n (n\geq 3) which are called isoptic hypersurfaces. We develope an algorithm to determine the isoptic hypersurface H_D of an arbitrary (n−1) dimensional compact parametric domain D lying in a hyperplane in the Euclidean n-space.
We will determine the equation of the isoptic hypersurfaces of rectangles D \subset E^2 and visualize them with Wolfram Mathematica. Moreover, we will show some possible
applications of the isoptic hypersurfaces.

Keywords

isoptic curves; hypersurfaces; differential geometry; elliptic geometry

Hrčak ID:

114277

URI

https://hrcak.srce.hr/114277

Publication date:

27.1.2014.

Article data in other languages: croatian

Visits: 1.517 *