Related papers: An Elementary Proof for the Basel Problem
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
Using a double integral we give another solution to the Basel Problem
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
The import of Bell's Theorem is elucidated. The theorem's proof is illustrated both heuristically and in mathematical detail in a pedagogical fashion. In the same fashion, it is shown that the proof is correct mathematically, but it doesn't…
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.
This paper is purely expositional. The statement of the Abel-Ruffini theorem on unsolvability of equations using radicals is simple and well-known. We sketch an elementary proof of this theorem. We do not use the terms 'field extension',…
A proof is given of Rosenthal's \(\ell_1\) theorem.
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
In the paper, in light of the generating function of the complete Bell polynomials and other techniques, the author presents concise and elegant proofs of three formulas for the complete Bell polynomials.
We present a new, elementary, dynamical proof of the prime number theorem.
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
We provide an elementary derivation of the Bessel analog of the celebrated Riesz composition formula and use the former to effortlessly derive the latter.
An elementary proof of an identity by Lyons, Paule and Riese is given. It is simpler than all the 3 published proofs.
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
This paper contains a new elementary proof of the Fundamental Theorem of Calculus for the Lebesgue integral. The hardest part of our proof simply concerns the convergence in ${\rm L}^1$ of a certain sequence of step functions, and we prove…
We will give a simple proof of the ambiguous class number formula.
We evaluate several arctangent and logarithmic integrals depending on a parameter. This provides a closed form summation of certain series and also gives integral and series representation of some classical constants.
We give a new simpler proof of a theorem of Jayne and Rogers.
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.