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Journal for Geometry and Graphics 25 (2021), No. 1, 127--137 Copyright Heldermann Verlag 2021 A Quadratic Mapping Related to Frégier's Theorem and Some Generalisations Gunter Weiß Technische Universität, Dresden, Germany and: University of Technology, Vienna, Austria weissgunter@gmx.at Pavel Pech Faculty of Education, University of South Bohemia, Ceske Budejovice, Czech Republic pech@pf.jcu.cz We start with a special Steiner's generation of a conic section based on a quadratic mapping, which is connected to a well-known theorem of Frégier. The paper generalises this construction of a conic to higher dimensions and to algebraic mappings of higher order. Keywords: Conic section, Steiner's generation, Fregier point, quadratic mapping. MSC: 51Mxx; 51N15, 51N20, 51N35. [ Fulltext-pdf (986 KB)] |