Beni Bogoşel's blog

On this page I have posted some of my research projects and articles.

The following article is inspired from a problem given in a “Traian Lalescu” contest. Surprisingly, from what I’ve heard, the problem didn’t have a solution then. When studying the proof of Sierpinski’s theorem which states that any function can be written as the sum of two Darboux functions, I came up with the proof for the old problem. The details are in the article.
Functii ciudate
The problem I speak about is solved separately here. The article above has many more details. I proposed the problem for AMM, but they said it’s too hard to publish it alone.
Darboux Problem

This is a problem inspired from the van der Waerden Theorem. The proof given here uses the one dimensional van der Waerden Theorem, but the problem itself is a particular care of the two dimensional van der Waerden Theorem.
Coloring of the Plane (Romanian)

Below is a cute proof of Thales’s Theorem.
Thales (Romanian)

Below are two proofs of important properties of infinite cardinal numbers. (both in Romanian)
Numere cardinale x+x=x
Numere cardinale x.x=x

The following problem was proposed and published in AMM by myself and Cezar Lupu.
Matrix Inequality

This is a problem set, with problems composed or modified by myself. (Romanian)
Problems

This is probably a new proof of Euler’s Polyhedron Formula.
Euler Proof

Graduation paper. (Romanian)
Beniamin Bogosel-Lucrare de licenta

Master final paper (English) – these