Journal for Geometry and Graphics 7 (2003), No. 1, 023--039
Copyright Heldermann Verlag 2003
Curves related to triangles: The Balaton-Curves
Institute for Mathematics, University of Klagenfurt, Universitätsstr. 65-67, 9020 Klagenfurt, Austria, email@example.com
Institute for Mathematics, University of Klagenfurt, Universitätsstr. 65-67, 9020 Klagenfurt, Austria, firstname.lastname@example.org
The remarkable points orthocentre H, circumcentre U, in-centre I, Torricelli's point T1 and the first isodynamic point D1 of a given triangle Δ in the Euclidean plane lie on a naturally defined curve f which we call the Balaton-curve of Δ. We determine all triangles for which this curve is algebraic and investigate it when it is algebraic, and when it is transcendental as well. In the algebraic case we determine its irreducible equation in the projective plane over C.
Keywords: triangle, Balaton-curve.
MSC: 51M04, 51N35.
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