Orthoptic Sets and Quadric Hypersurfaces

Year 2021, Volume: 4 Issue: 3, 130 - 136, 30.09.2021

François Dubeau

https://doi.org/10.33434/cams.917192

Abstract

Orthoptic curves for the conics are well known.
It is the Monge's circle for ellipse and hyperbola, and for parabola it is its directrix.
These conics are level sets of quadratic functions in the plane.
We consider level sets of quadratic functions in higher dimension, known as quadric hypersurfaces.
For these hypersurfaces we present and study their orthoptic sets, which extend the idea of orthoptic curves for conics.

Keywords

orthoptic set, directrix, Monge's circle, quadric hypersurface

Supporting Institution

Université de Sherbrooke, NSERC (Natural Sciences and Engineering Research Council of Canada)

Thanks

This work has been financially supported by an individual discovery grant from NSERC (Natural Sciences and Engineering Research Council of Canada)

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