Related papers: Pythagorean theorem from Heron's formula: Another …
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 present an elementary proof for Ljunggren equation
We give a proof of Pythagoras' theorem which does not use neither squares nor similarity of triangles.
This article studies the application of the Pythagorean theorem in the Susa Mathematical Texts (\textbf{SMT}) and we discuss those texts whose problems and related calculations demonstrate its use. Among these texts, \textbf{SMT No.\,1}…
In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.
By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.
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…
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
An elementary derivation of the Newton "inverse square law" from the three Kepler laws is proposed. Our proof, thought essentially for first-year undergraduates, basically rests on Euclidean geometry. It could then be offered even to…
This article highlights interactions of diverse areas: the Heron formula for the area of a triangle, the Descartes circle equation, and right triangles with integer or rational sides. New and old results are synthesized. We show that every…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
We previously extended the Marsden-Ratiu reduction theorem in Poisson geometry by means of graded geometry (see Part I of Arxiv:1009.0948) . In this note we provide the background material about graded geometry necessary for the proof.…
In this article, we derive the Helton-Howe-Carey-Pincus trace formula as a consequence of Krein's trace formula.
In this paper, we present the Baumkuchen Theorem related to the combination of divided Baumkuchen pieces. It can be proved using the basic properties of elementary geometry. We also apply some lemmas to prove the Pizza Theorem.
In this short paper we review and extract some features of the Fredholm Alternative problem .
We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…