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 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 
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     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},
     year = {2018},
     volume = {22},
     number = {1},
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}
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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/