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Journal for Geometry and Graphics 7 (2003), No. 1, 023--039
Copyright Heldermann Verlag 2003
Curves related to triangles: The Balaton-Curves
H. Dirnböck
Institute for Mathematics, University of Klagenfurt, Universitätsstr. 65-67, 9020 Klagenfurt,
Austria, hans.dirnboeck@uni-klu.ac.at
J. Schoißengeier
Institute for Mathematics, University of Klagenfurt, Universitätsstr. 65-67, 9020 Klagenfurt, Austria,
johannes.schoissengeier@uni-klu.ac.at
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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