Related papers: Geometric visualizations of $b^{e}<e^{b}$ when $e<…
We extend the classical results of Stanislaw Golab, on the values of pi in arbitrary normed planes, to asymmetric norms where the unit ball has one axis of symmetry. First, we characterize the values of $\pi_B$ for different families of…
Various Bell inequalities are trivial algebraic properties satisfied by each line of particular data spreadsheets.It is surprising that their violation in some experiments, allows to speculate about the existence of nonlocal influences in…
We introduce a class of surfaces in euclidean space motivated by a problem posed by \'{E}lie Cartan. This class furnishes what seems to be the first examples of pairs of non-congruent surfaces in euclidean space such that, under a…
This article discusses how to make statistical graphics a more prominent element of the undergraduate statistics curricula. The focus is on several different types of assignments that exemplify how to incorporate graphics into a course in a…
We present a complete classification of minimal problems for generic arrangements of points and lines in space observed partially by three calibrated perspective cameras when each line is incident to at most one point. This is a large class…
The constant $\pi$ has fascinated scholars throughout the centuries, inspiring numerous formulas for its evaluation, such as infinite sums and continued fractions. Despite their individual significance, many of the underlying connections…
We suggest an unified presentation to teach fundamental constants to graduate students, by introducing four lower limits to observed phenomena. The reduced Planck constant $\hbar$ is the lowest classically definable action. The inverse of…
In the paper, the authors establish some best approximation formulas and inequalities for Wallis ratio. These formulas and inequalities improve an approximation formula and a double inequality for Wallis ratio recently presented in ``S.…
Visualizations that adopt a first-person point of view allow observation and, in the case of interactive simulations, experimentation with relativistic scenes. This paper gives examples of three types of first-person visualizations:…
We consider the gravity field of a Bose-Einstein condensate in a quantum superposition. The gravity field then is also in a quantum superposition which is in principle observable. Hence we have ``quantum gravity'' far away from the…
The paper consider an equivalence relation in the set of vertices of a bipartite graph. Some numerical characteristics showing the cardinality of equivalence classes are introduced. A combinatorial identity that is in relationship to these…
We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio…
Comparison of answers offered by a computer algebra system (CAS) with answers derived by a student without a CAS is relevant, for instance, in the context of computer-aided assessment (CAA). The issues of identity, equivalence and…
We provide a pipeline for calculating, managing and visualising correlations and other pairwise association scores for numerical and categorical data. We present a uniform interface for calculating a plethora of pairwise scores and propose…
This paper examines the quantum mechanical system that arises when one quantises a classical mechanical configuration described by an underdetermined system of equations. Specifically, we consider the well-known problem in classical…
Infographics are a form of data visualization combining data, information, and statistics. Over the last ten years, infographics have become a popular method for displaying concise information, where infographics are a useful tool for…
Attempting to create a general framework for studying new results on transcendental numbers, this paper begins with a survey on transcendental numbers and transcendence, it then presents several properties of the transcendental numbers $e$…
A number of results for C$^2$-smooth surfaces of constant width in Euclidean 3-space ${\mathbb{E}}^3$ are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of…
In this essay I begin to lay out a conceptual scheme for: (i) analysing dualities as cases of theoretical equivalence; (ii) assessing when cases of theoretical equivalence are also cases of physical equivalence. The scheme is applied to…
We provide a quantitative observability inequality for the von Neumann equation on $\mathbb{R}^d$ in the crystal setting, uniform in small $\hbar$. Following the method of Golse and Paul (2022) proving this result in the non-crystal…