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

How was this proof overlooked for 181 years? We give a simple proof of Descartes's circle theorem using Cayley-Menger determinants.

A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…

We reformulate, in the context of continuous logic, an oscillation theorem originally proved by G. Hjorth. We give a proof of the theorem in that setting which is similar to, but simpler than, Hjorth's original one. The point of view…

We propose an interpretation of the Newton's second law that is suggested by Galilean Relativity theory.

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

An equivalent but useful version on the Homological Nerve Theorem is proved.

The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…

Inspired by a recent preprint of N. Curien, we provided what may be a new and elementary proof of the Law of Large Numbers.

An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in…

The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.

We give a simple proof of Bourgain's theorem on the singularity of Ornstein's maps.

The issue and proof of Gurzadyan theorem are presented concisely, avoiding tedious and unnecessary calculations that would mask what is essential. The goal is to provide a good mathematical and physical understanding of the theorem, making…

We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…

We give a purely combinatorial proof of the density Hales--Jewett Theorem that is modeled after Polymath's proof but is significantly simpler. In particular, we avoid the use of the equal-slices measure and work exclusively with the uniform…

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

We prove an infinitary version of the Brauer-Schur theorem.

In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.