Orthoptic Sets and Quadric Hypersurfaces
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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