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Journal for Geometry and Graphics 18 (2014), No. 2, 199--203
Copyright Heldermann Verlag 2014

Surprising Relations Between the Areas of Triangles in the Configuration of Routh's Theorem

Viktor Oxman
Western Galilee College, P.O.B. 2125, Acre 24121, Israel

Moshe Stupel
Shaanan College, P.O.B. 906, Haifa 26109, Israel

Avi Sigler
Technical College for Aviation Professions, Haifa, Israel

The paper considers some extremum problems related to the ratio of the areas of triangles formed by the intersection of three cevians in connection with Routh's Theorem. The solution of the problems brings surprising results related to the golden ratio.

Keywords: Routh's Theorem, triangle's area, extremum problems, golden ratio.

MSC: 51M05; 51M16

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