KoG, Vol. 19. No. 19., 2015.
Izvorni znanstveni članak
Elementary Constructions for Conics in Hyperbolic and Elliptic Planes
Gunter Weiss
; University of Technology Vienna, Vienna, Austria
Sažetak
In the Euclidean plane there are well-known constructions of points and tangents of e.g. an ellipse c based on the given axes of c, which make use of the Apollonius definition of c via its focal points or via two perspective anities (de la Hire's construction). Even there is no parallel relation neither in a hyperbolic plane nor in an elliptic plane it is still possible to modify many of the elementary geometric constructions for conics, such that they also hold for those (regular) non-Euclidean planes. Some of these modications just replace Euclidean straight lines by non-Euclidean circles. Furthermore we also study properties of Thales conics, which are generated by two pencils of (non-Euclidean) orthogonal lines.
Ključne riječi
hyperbolic plane; elliptic plane; conic sections; de la Hire; Apollonius; Thales
Hrčak ID:
151332
URI
Datum izdavanja:
19.1.2016.
Posjeta: 1.322 *