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The Parabola in Universal Hyperbolic Geometry I

Ali Alkhaldi ; School of Mathematics and Statistics UNSW, Sydney, Australia
Norman John Wildberger orcid id ; School of Mathematics and Statistics UNSW, Sydney, Australia

Puni tekst: engleski pdf 606 Kb

str. 14-42

preuzimanja: 1.007



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

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