Geodesic
From M. C. Escher's Hexagonal Tiling to the Kiepert Hyperbola
Journal for geometry and graphics, Tome 25 (2021) no. 1, pp. 79-95.

Voir la notice de l'article provenant de la source Heldermann Verlag

Generalizing Fermat and Napoleon points of a triangle, we introduce the notion of complementary Jacobi points, showing their collinearity with the circumcenter of the given triangle. The coincidence of the associated perspective lines for complementary Jacobi points is also proved, together with the orthogonality of this line with the one joining the circumcenter and the Jacobi points. Involutions on the Kiepert hyperbola naturally arise, allowing a geometric insight on the relationship between Jacobi points, their associated perspective lines and Kiepert conics of a triangle.
Classification : 51M04, 00A66
Mots-clés : Triangle geometry, Escher, Napoleon Point, Fermat Point, Kiepert hyperbola 
@article{JGG_2021_25_1_JGG_2021_25_1_a7,
     author = {F. Giudiceandrea and L. Grasselli },
     title = {From {M.} {C.} {Escher's} {Hexagonal} {Tiling} to the {Kiepert} {Hyperbola}},
     journal = {Journal for geometry and graphics},
     pages = {79--95},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2021},
     url = {http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a7/}
}
TY  - JOUR
AU  - F. Giudiceandrea
AU  - L. Grasselli 
TI  - From M. C. Escher's Hexagonal Tiling to the Kiepert Hyperbola
JO  - Journal for geometry and graphics
PY  - 2021
SP  - 79
EP  - 95
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a7/
ID  - JGG_2021_25_1_JGG_2021_25_1_a7
ER  - 
%0 Journal Article
%A F. Giudiceandrea
%A L. Grasselli 
%T From M. C. Escher's Hexagonal Tiling to the Kiepert Hyperbola
%J Journal for geometry and graphics
%D 2021
%P 79-95
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a7/
%F JGG_2021_25_1_JGG_2021_25_1_a7
F. Giudiceandrea; L. Grasselli . From M. C. Escher's Hexagonal Tiling to the Kiepert Hyperbola. Journal for geometry and graphics, Tome 25 (2021) no. 1, pp. 79-95. http://geodesic.mathdoc.fr/item/JGG_2021_25_1_JGG_2021_25_1_a7/