14 citations · 17 across the 16 of their papers we have counts for
4 papers · 1 filter
Ceva's triangle inequalities
Árpád Bényi, Branko Ćurgus
We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a three-parameter family of i…
A generalization of Routh's triangle theorem
Arpad Benyi, Branko Curgus
We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangl…
Triangles and groups via cevians
Árpád Bényi, Branko Ćurgus
For a given triangle and a real number we define Ceva's triangle $\CT_ρ(T)$ to be the triangle formed by three cevians each joining a vertex of to the point which divid…
On a Convex Operator for Finite Sets
Branko Ćurgus, Krzysztof Kołodziejczyk
Let be a finite set with elements in a real linear space. Let $\cJ_S$ be a set of intervals in $\nR$. We introduce a convex operator $\co(S,\cJ_S)$ which generalizes th…