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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 victor.oxman@gmail.com Moshe Stupel Shaanan College, P.O.B. 906, Haifa 26109, Israel stupel@bezeqint.net Avi Sigler Technical College for Aviation Professions, Haifa, Israel anysig@walla.co.il 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 [ Fulltext-pdf (89 KB)] for subscribers only. |