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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

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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