Related papers: Looking through newly to the amazing irrationals
New (infinitely many) rational approximants to \zeta(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A…
We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes such proofs can be fully automated, but…
Laymen and sometimes even physicists think of natural sciences, in particular of theoretical and mathematical physics often as subjects, which unfold according to an intrinsic logical pattern, with the limitations being set only by the…
Quadratic irrationals posses a periodic continued fraction expansion. Much less is known about cubic irrationals. We do not even know if the partial quotients are bounded, even though extensive computations suggest they might follow…
In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
In this note we show that in addition to two integers forming a Pythagorean triple, there also exist two irrational numbers in terms of which this Pythagorean triple can also be obtained. We also put forward a relation between these two…
We show that there exists a natural counterpart of the Gromov-Hausdorff metric in the class of ultrametric spaces. It is proved, in particular, that the space of all ultrametric spaces whose metric take values in a fixed countable set is…
One of the most stimulating recent ideas in particle physics involves a possibility that our universe has additional compactified spatial dimensions, perhaps as large as 1 mm. In this review, we discuss the results of recent experimental…
Continued fractions are used to give an alternate proof of $e^{x/y}$ is irrational.
The extravagances of quantum mechanics never fail to enrich daily the debate around natural philosophy. Entanglement, non-locality, collapse, many worlds, many minds, and subjectivism have challenged generations of thinkers. Its approach…
One of the most stimulating recent ideas in particle physics involves a possibility that our universe has additional compactified spatial dimensions, perhaps as large as 1 mm. In this mini-review, we discuss the results of recent…
In this paper we make some observations concerning m-metric spaces and point out some discrepancies in the proofs found in the literature. To remedy this, we propose a new topological construction and prove that it is in fact a…
The field of neutrino physics is currently very exciting, with several recent results pointing to new physics. I will give an overview of the current experimental situation, focusing primarily on neutrino oscillation results. The data are…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…
Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this…
The purpose of this new survey paper is, among other things, to collect in one place most of the articles on cone (abstract, K-metric) spaces, published after 2007. This list can be useful to young researchers trying to work in this part of…
A new theory of fundamental physics is presented; it predicts that the new dimensions that may be observed by the Large Hadron Collider are timelike.
We provide an alternative proof that $\sqrt{2}$ is irrational that does not begin with the assumption that $\sqrt{2}$ is in fact rational.