Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 275-282 (1999)

A Noteworthy Property of the Tridens Curve in the Isotropic Plane

Jürgen Tölke

Fachbereich Mathematik, Universität Siegen, Hölderlinstrasse 3, D-57068 Siegen, Germany

Abstract: We consider the pencil P of the cubic parabolas through the vertices of a triangle $\Delta$ in the isotropic plane. The locus of the inflection points is a tridens curve T of third order through the vertices and the side-midpoints of $\Delta $. Every tridens curve has such inscribed triangles $\Delta$. They are formed by the points of contact of the non-isotropic tangents of T which pass through a point of the asymptote of the tridens curve.

Keywords: isotropic plane, cubic parabolas, inflection points, tridens curves of third order

Classification (MSC91): 51N25

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