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Journal for Geometry and Graphics 20 (2016), No. 1, 001--011
Copyright Heldermann Verlag 2016



The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Y-conic

Ali Alkhaldi
Dept. of Mathematics, King Khalid University, 61431 Asir - Abha, Saudi Arabia
ahalkhaldi@kku.edu.sa

Norman J. Wildberger
School of Mathematics and Statistics, University of New South Wales, Sydney 2052 NSW, Australia
n.wildberger@unsw.edu.au



We introduce canonical points and lines for the hyperbolic parabola in Universal Hyperbolic Geometry, and explicit formulas for them in standard coordinates. Quite a few remarkable collinearities result, with the duality of the twin parabola playing a major role. We also introduce the curious Y-conic which is homologous to the parabola, and contains many interesting meets.

Keywords: Hyperbolic geometry, projective geometry, universal geometry, hyperbolic parabola.

MSC: 51M10; 51N15, 14N99

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