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Elementary Constructions for Conics in Hyperbolic and Elliptic Planes

Gunter Weiss ; University of Technology Vienna, Vienna, Austria

Puni tekst: engleski, pdf (2 MB) str. 24-31 preuzimanja: 418* citiraj
APA 6th Edition
Weiss, G. (2015). Elementary Constructions for Conics in Hyperbolic and Elliptic Planes. KoG, 19. (19.), 24-31. Preuzeto s https://hrcak.srce.hr/151332
MLA 8th Edition
Weiss, Gunter. "Elementary Constructions for Conics in Hyperbolic and Elliptic Planes." KoG, vol. 19., br. 19., 2015, str. 24-31. https://hrcak.srce.hr/151332. Citirano 25.01.2020.
Chicago 17th Edition
Weiss, Gunter. "Elementary Constructions for Conics in Hyperbolic and Elliptic Planes." KoG 19., br. 19. (2015): 24-31. https://hrcak.srce.hr/151332
Harvard
Weiss, G. (2015). 'Elementary Constructions for Conics in Hyperbolic and Elliptic Planes', KoG, 19.(19.), str. 24-31. Preuzeto s: https://hrcak.srce.hr/151332 (Datum pristupa: 25.01.2020.)
Vancouver
Weiss G. Elementary Constructions for Conics in Hyperbolic and Elliptic Planes. KoG [Internet]. 2015 [pristupljeno 25.01.2020.];19.(19.):24-31. Dostupno na: https://hrcak.srce.hr/151332
IEEE
G. Weiss, "Elementary Constructions for Conics in Hyperbolic and Elliptic Planes", KoG, vol.19., br. 19., str. 24-31, 2015. [Online]. Dostupno na: https://hrcak.srce.hr/151332. [Citirano: 25.01.2020.]

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 defi nition 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 modi cations 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
https://hrcak.srce.hr/151332

[hrvatski]

Posjeta: 552 *