Geodesic
Curves related to triangles: The Balaton-Curves
Journal for geometry and graphics, Tome 7 (2003) no. 1, pp. 023-04 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 
@article{JGG_2003_7_1_JGG_2003_7_1_a1,
     author = {H. Dirnb�ck and J. Schoi�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/}
}
TY  - JOUR
AU  - H. Dirnb�ck
AU  - J. Schoi�engeier
TI  - Curves related to triangles: The Balaton-Curves
JO  - Journal for geometry and graphics
PY  - 2003
SP  - 023
EP  - 04
VL  - 7
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JGG_2003_7_1_JGG_2003_7_1_a1/
ID  - JGG_2003_7_1_JGG_2003_7_1_a1
ER  - 
%0 Journal Article
%A H. Dirnb�ck
%A J. Schoi�engeier
%T Curves related to triangles: The Balaton-Curves
%J Journal for geometry and graphics
%D 2003
%P 023-04
%V 7
%N 1
%U http://geodesic.mathdoc.fr/item/JGG_2003_7_1_JGG_2003_7_1_a1/
%F JGG_2003_7_1_JGG_2003_7_1_a1
H. Dirnb�ck; J. Schoi�engeier. 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/