Geodesic
The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Y-conic
Journal for geometry and graphics, Tome 20 (2016) no. 1, pp. 1-11

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

We introduce canonical points and lines for the hyperbolic parabola in Universal Hyperbolic Geometry, and explicit formulas for them in standard coordinates. Quite a few remarkable collinearities result, with the duality of the twin parabola playing a major role. We also introduce the curious Y-conic which is homologous to the parabola, and contains many interesting meets.
Classification : 51M10, 51N15, 14N99
Mots-clés : Hyperbolic geometry, projective geometry, universal geometry, hyperbolic parabola 
A. Alkhaldi; N. J. Wildberger. The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Y-conic. Journal for geometry and graphics, Tome 20 (2016) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/JGG_2016_20_1_JGG_2016_20_1_a0/
@article{JGG_2016_20_1_JGG_2016_20_1_a0,
     author = {A. Alkhaldi and N. J. Wildberger},
     title = {The {Parabola} in {Universal} {Hyperbolic} {Geometry.} {II:} {Canonical} {Points} and the {Y-conic}},
     journal = {Journal for geometry and graphics},
     pages = {1--11},
     year = {2016},
     volume = {20},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2016_20_1_JGG_2016_20_1_a0/}
}
TY  - JOUR
AU  - A. Alkhaldi
AU  - N. J. Wildberger
TI  - The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Y-conic
JO  - Journal for geometry and graphics
PY  - 2016
SP  - 1
EP  - 11
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JGG_2016_20_1_JGG_2016_20_1_a0/
ID  - JGG_2016_20_1_JGG_2016_20_1_a0
ER  - 
%0 Journal Article
%A A. Alkhaldi
%A N. J. Wildberger
%T The Parabola in Universal Hyperbolic Geometry. II: Canonical Points and the Y-conic
%J Journal for geometry and graphics
%D 2016
%P 1-11
%V 20
%N 1
%U http://geodesic.mathdoc.fr/item/JGG_2016_20_1_JGG_2016_20_1_a0/
%F JGG_2016_20_1_JGG_2016_20_1_a0