历史与综述
Cars arrive at an intersection with a stoplight, which is either red or green. The cars all travel in the same direction, that is, we ignore cross-traffic & oncoming traffic. Assume that the intersection is initially empty. Assume that, at…
This elementary treatment first summarizes extreme values of a Bernoulli random walk on the one-dimensional integer lattice over a finite discrete time interval. Both the symmetric (unbiased) and asymmetric (biased) cases are discussed.…
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
In this article we provide several exact formulae to calculate the probability that a random triangle chosen within a planar region (any Lebesgue measurable set of finite measure) contains a given fixed point $O$. These formulae are in…
We generalize problems in Wasan geometry which involve no folded figures but are related to Haga's fold in origami. Using the tangent circles appeared in those problems we give a parametric representation of the generalized Haga's fold…
We construct random triangles via uniform sampling of certain families of lines in the plane. Two examples are given. The word "uniform" turns out to be vague; two competing models are examined. Everything we write is well-known to experts.…
We describe our adventures in creating a new first-year course in Experimental Mathematics that uses active learning. We used a state-of-the-art facility, called The Western Active Learning Space, and got the students to "drive the…
We introduce Partiti, the puzzle that will run in Mathematics Magazine in 2018, and use the opportunity to recall some basic properties of integer partitions.
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
In this paper, the authors design a trial to count rational ratios on the interval [0, 1], and plot a normalized frequency statistical graph. Patterns, symmetry and co-linear properties reflected in the graph are confirmed. The main…
We prove that there exists a geodesic trajectory on the dodecahedron from a vertex to itself that does not pass through any other vertex.
Testing convergence of infinite series is an important part of mathematics. A very basic test of convergence is to upper-bound a given series with a known series, term by term. In $19^{th}$ century, Kummer proposed a test of convergence for…
We obtain an important generalization of the mechanical solution given by S. Gueron and R. Tessler w.r. to the weighted Fermat-Torricelli problem which derives a new structure of solutions which may be called oscillatory Fermat-Torricelli…
The problem of finding formulas for sums of powers of natural numbers has been of interest to mathematicians for many centuries. Among these is Faulhaber's well-known formula expressing the power sums as polynomials whose coefficients…
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus,…
This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic…
The present is a companion paper to "A contemporary look at Hermann Hankel's 1861 pioneering work on Lagrangian fluid dynamics" by Frisch, Grimberg and Villone (2017). Here we present the English translation of the 1861 prize manuscript…
The present paper is a companion to the paper by Villone and Rampf (2017), titled "Hermann Hankel's On the general theory of motion of fluids, an essay including an English translation of the complete Preisschrift from 1861" together with…