Geodesic
Curves related to triangles: The Balaton-Curves
Journal for geometry and graphics, Tome 7 (2003) no. 1, pp. 023-04
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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.
Classification : 51M04, 51N35
Mots-clés : triangle, Balaton-curve 
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     author = {H. Dirnb\"ock and J. Schoi{\ss}engeier},
     title = {Curves related to triangles: {The} {Balaton-Curves}},
     journal = {Journal for geometry and graphics},
     pages = {023--04},
     year = {2003},
     volume = {7},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2003_7_1_JGG_2003_7_1_a1/}
}
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H. Dirnböck; J. Schoißengeier. Curves related to triangles: The Balaton-Curves. Journal for geometry and graphics, Tome 7 (2003) no. 1, pp. 023-04. http://geodesic.mathdoc.fr/item/JGG_2003_7_1_JGG_2003_7_1_a1/