Geodesic
Generalization of the Pappus Theorem in the Plane and in Space
Journal for geometry and graphics, Tome 22 (2018) no. 1, pp. 59-66.

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

One of the Pappus theorems states that if points F, E, D divide the sides of triangle ABC in the same ratio α, then the triangles ABC and FED have the same centroid. Therefore, the intersection Q of such triangles FED obtained for all non-negative α, is not empty. In this paper we will characterize the domain Q for the general case of dividing the sides of a triangle (not necessary in the same ratio) and prove that Q is bound by conic sections. We will also present some surprising results concerning Q for the case of a tetrahedron.
Classification : 51M05
Mots-clés : Pappus Theorem, triangle, tetrahedron, conic sections 
@article{JGG_2018_22_1_JGG_2018_22_1_a6,
     author = {V. Oxman and A. Sigler and M. Stupel },
     title = {Generalization of the {Pappus} {Theorem} in the {Plane} and in {Space}},
     journal = {Journal for geometry and graphics},
     pages = {59--66},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/JGG_2018_22_1_JGG_2018_22_1_a6/}
}
TY  - JOUR
AU  - V. Oxman
AU  - A. Sigler
AU  - M. Stupel 
TI  - Generalization of the Pappus Theorem in the Plane and in Space
JO  - Journal for geometry and graphics
PY  - 2018
SP  - 59
EP  - 66
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JGG_2018_22_1_JGG_2018_22_1_a6/
ID  - JGG_2018_22_1_JGG_2018_22_1_a6
ER  - 
%0 Journal Article
%A V. Oxman
%A A. Sigler
%A M. Stupel 
%T Generalization of the Pappus Theorem in the Plane and in Space
%J Journal for geometry and graphics
%D 2018
%P 59-66
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JGG_2018_22_1_JGG_2018_22_1_a6/
%F JGG_2018_22_1_JGG_2018_22_1_a6
V. Oxman; A. Sigler; M. Stupel . Generalization of the Pappus Theorem in the Plane and in Space. Journal for geometry and graphics, Tome 22 (2018) no. 1, pp. 59-66. http://geodesic.mathdoc.fr/item/JGG_2018_22_1_JGG_2018_22_1_a6/