Geodesic
A New Generalization of the Butterfly Theorem
Journal for geometry and graphics, Tome 6 (2002) no. 1, pp. 061-068 Cet article a éte moissonné depuis la source Heldermann Verlag

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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. 
@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/}
}
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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/