hrcak mascot   Srce   HID

Izvorni znanstveni članak

The Parabola in Universal Hyperbolic Geometry I

Ali Alkhaldi ; School of Mathematics and Statistics UNSW, Sydney, Australia
Norman John Wildberger   ORCID icon orcid.org/0000-0003-3503-6495 ; School of Mathematics and Statistics UNSW, Sydney, Australia

Puni tekst: engleski, pdf (606 KB) str. 14-42 preuzimanja: 646* citiraj
APA 6th Edition
Alkhaldi, A. i Wildberger, N.J. (2013). The Parabola in Universal Hyperbolic Geometry I. KoG, 17. (17.), 14-42. Preuzeto s https://hrcak.srce.hr/114271
MLA 8th Edition
Alkhaldi, Ali i Norman John Wildberger. "The Parabola in Universal Hyperbolic Geometry I." KoG, vol. 17., br. 17., 2013, str. 14-42. https://hrcak.srce.hr/114271. Citirano 23.01.2020.
Chicago 17th Edition
Alkhaldi, Ali i Norman John Wildberger. "The Parabola in Universal Hyperbolic Geometry I." KoG 17., br. 17. (2013): 14-42. https://hrcak.srce.hr/114271
Harvard
Alkhaldi, A., i Wildberger, N.J. (2013). 'The Parabola in Universal Hyperbolic Geometry I', KoG, 17.(17.), str. 14-42. Preuzeto s: https://hrcak.srce.hr/114271 (Datum pristupa: 23.01.2020.)
Vancouver
Alkhaldi A, Wildberger NJ. The Parabola in Universal Hyperbolic Geometry I. KoG [Internet]. 2013 [pristupljeno 23.01.2020.];17.(17.):14-42. Dostupno na: https://hrcak.srce.hr/114271
IEEE
A. Alkhaldi i N.J. Wildberger, "The Parabola in Universal Hyperbolic Geometry I", KoG, vol.17., br. 17., str. 14-42, 2013. [Online]. Dostupno na: https://hrcak.srce.hr/114271. [Citirano: 23.01.2020.]

Sažetak
We introduce a novel definition of a parabola into the framework of universal hyperbolic geometry, show many analogs with the Euclidean theory, and also some remarkable new features. The main technique is to establish parabolic standard coordinates in which the parabola has
the form xz = y^2. Highlights include the discovery of the twin parabola and the connection with sydpoints, many unexpected concurrences and collinearities, a construction for the evolute, and the determination of (up to) four points on the parabola whose normals meet.

Ključne riječi
universal hyperbolic geometry; parabola

Hrčak ID: 114271

URI
https://hrcak.srce.hr/114271

[hrvatski]

Posjeta: 887 *