Original scientific paper

The Parabola in Universal Hyperbolic Geometry I

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

Abstract

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.

Keywords

universal hyperbolic geometry; parabola

Hrčak ID:

114271

URI

https://hrcak.srce.hr/114271

Publication date:

27.1.2014.

Article data in other languages: croatian

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