Related papers: A Special Theorem Related to the Fagnano's Problem

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena

In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.

The golden ratio is usually shrouded in mystique and mystery, however, showing its emergence from a familiar geometric setting makes it a more natural phenomenon. In this work, we present a new theorem connecting the Tangent Secant theorem…

By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

By using Fubini theorem or Tonelli theorem, we find that the zeta function value at 2 is equal to a special integral. Furthermore, We find that this special integral is two times of another special integral. By using this fact we obtain the…

We obtain some results related to Romanoff's theorem.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

We extend Haran's Diamond Theorem to closed subgroups of a finitely generated free profinite group. This gives an affirmative answer to Problem 25.4.9 in the book Field Arithmetics of Fried and Jarden.

We show that a single special separation theorem (namely, a consequence of the geometric form of the Hahn-Banach theorem) can be used to prove Farkas type theorems, existence theorems for numerical quadrature with positive coefficients, and…

There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem…

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

A proof is given of Rosenthal's \(\ell_1\) theorem.

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 concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

In this note we give a detailed proof of a theorem of Aubin.

A weak bialgebra is known to be a special case of a bialgebroid. In this paper we study the relationship of this fact with the Tannaka theory of bialgebroids as developed in [4]. We obtain a Tannaka representation theorem with respect to a…

In fuzzy group theory many versions of the well-known Lagrange's theorem have been studied. The aim of this article is to investigate the converse of one of those results. This leads to an interesting characterization of finite cyclic…