Geodesic
A New Generalization of the Butterfly Theorem
Journal for geometry and graphics, Tome 6 (2002) no. 1, pp. 061-068 
A. Sliepcevic. A New Generalization of the Butterfly Theorem. Journal for geometry and graphics, Tome 6 (2002) no. 1, pp. 061-068. http://geodesic.mathdoc.fr/item/JGG_2002_6_1_a4/
@article{JGG_2002_6_1_a4,
     author = {A. Sliepcevic},
     title = {A {New} {Generalization} of the {Butterfly} {Theorem}},
     journal = {Journal for geometry and graphics},
     pages = {061--068},
     year = {2002},
     volume = {6},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2002_6_1_a4/}
}
TY  - JOUR
AU  - A. Sliepcevic
TI  - A New Generalization of the Butterfly Theorem
JO  - Journal for geometry and graphics
PY  - 2002
SP  - 061
EP  - 068
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JGG_2002_6_1_a4/
ID  - JGG_2002_6_1_a4
ER  - 
%0 Journal Article
%A A. Sliepcevic
%T A New Generalization of the Butterfly Theorem
%J Journal for geometry and graphics
%D 2002
%P 061-068
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/JGG_2002_6_1_a4/
%F JGG_2002_6_1_a4

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

The butterfly theorem and some of its generalizations deal with a specific point related to a quadrangle inscribed into a circle. By use of the Sturm-Desargues involution theorem it is proved that with any such quadrangle an infinite number of butterfly points is associated which are located on an equilateral hyperbola. Finally an infinite number of quadrangles sharing the same butterfly curve is presented.