
Journal for Geometry and Graphics 7 (2003), No. 1, 023039 Copyright Heldermann Verlag 2003 Curves related to triangles: The BalatonCurves H. Dirnböck Institute for Mathematics, University of Klagenfurt, Universitätsstr. 6567, 9020 Klagenfurt, Austria, hans.dirnboeck@uniklu.ac.at J. Schoißengeier Institute for Mathematics, University of Klagenfurt, Universitätsstr. 6567, 9020 Klagenfurt, Austria, johannes.schoissengeier@uniklu.ac.at The remarkable points orthocentre H, circumcentre U, incentre I, Torricelli's point T_{1} and the first isodynamic point D_{1} of a given triangle Δ in the Euclidean plane lie on a naturally defined curve f which we call the Balatoncurve 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, Balatoncurve. MSC: 51M04, 51N35. FullTextpdf (1082 KB) for subscribers only. 