Related papers: Yet another elementary proof of Morley's theorem

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

We give a new simpler proof of a theorem of Jayne and Rogers.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.

A very simple but useful almost sure convergence theorem of probability is given.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

We establish a simple generalization for the famous theorem of Morley about trisectors in triangle with a purely synthetic proof using only angle chasing and similar triangles. Furthermore, based on the converse construction, another simple…

We give an elementary proof to Hasse theorem.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

We provide a simple proof of Kamp's theorem.

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.

We present a new, elementary, dynamical proof of the prime number theorem.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.