Journal for Geometry and Graphics 22 (2018), No. 1, 059--066
Copyright Heldermann Verlag 2018
Generalization of the Pappus Theorem in the Plane and in Space
Victor Oxman
Western Galilee College, P.O.B. 2125, Acre 24121, Israel
victor.oxman@gmail.com
Avi Sigler
Shaanan College, P.O.B. 906, Haifa 26109, Israel
Moshe Stupel
Shaanan College, P.O.B. 906, Haifa 26109, Israel
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.
Keywords: Pappus Theorem, triangle, tetrahedron, conic sections.
MSC: 51M05
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