历史与综述
We provide a faithful translation of Hans Richter's important 1948 paper "Das isotrope Elastizit\"atsgesetz" from its original German version into English. Our introduction summarizes Richter's achievements.
This short paper gives another proof of the infinitude of primes by using upper box dimension, which is one of fractal dimensions.
In continuous time, customers arrive at random. Each waits until one of $c$ servers is available; each thereafter departs at random. The distribution of maximum line length of idle customers was studied over 25 years ago. We revisit two…
The "free rider" problem has long plagued pedagogies based on collaborative learning. The most common solution to the free rider problem is peer evaluation. As well other existing methods of peer evaluation include self-evaluation --- and…
We formulate and prove a criterion for reducibility of a quadratic polynomial over the integers. The main theorem was suggested by the teaching experience with the concrete material called "the polynomial box". Through the corollaries we…
We analyze the set of increasingly enumerable additive submonoids of R, for instance, the set of logarithms of the positive integers with respect to a given base. We call them $\omega$-monoids. The $\omega$-monoids for which consecutive…
We establish some new constructions of the golden ratio in an arbitrary triangle using symmedians and nine-point circle.
The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…
In this note we will use Faulhaber's Formula to explain why the odd Bernoulli numbers are equal to zero.
We use Taylor's formula with Lagrange remainder to make a modern adaptation of Poisson's proof of a version of the fundamental theorem of calculus in the case when the integral is defined by Euler sums, that is Riemann sums with left (or…
\'Elie Cartan's "g\'en\'eralisation de la notion de courbure" (1922) arose from a creative evaluation of the geometrical structures underlying both, Einstein's theory of gravity and the Cosserat brothers generalized theory of elasticity. In…
This paper discusses a problem that consists of $n$ "lighthouses" which are circles with radius 1, placed around a common center, equidistant at $n$ units away from the placement center. Consecutive lighthouses are separated by the same…
In this paper, we analyze an aid session tested by an elementary school teachers. This aid session has been set up by a teacher for some students with difficulties after the work in the whole class. We first show how this aid session can…
In this communication we study a device set up to school deaf pupils. We analyze some sessions of mathematics classroom in which participated these pupils. We show in particular that if all the pupils seem globally in phase, cycles of…
According to the Liber Memorialis of the University of Ghent, the Belgian mathematician Paul Mansion (1844-1919) has published more than 349 academic papers and books. For our part, we were able to calculate the correct number by using the…
We show that the classical equivalence of Euclid's parallel postulate and Playfair's axiom collapses in the absence of triangle congruence. In particular, we construct a non-SAS geometry that models the Playfair axiom but not the parallel…
Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend…
The book "A Course in Constructive Algebra" (1988) shows the way of understanding classical basic algebra in a constructive style similar to Bishop's Constructive Mathematics. Classical theorems are revisited, with a new flavour, and become…
In this article, we are interested in the life and scientific work of the Belgian mathematician Paul Mansion. The year 2019 marks the centenary of his passing. We bring some new insights into Paul Mansion's work thanks to his scientific…
As is well known, a graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Therefore, it is not surprising that many of the first results concerning graphs made reference to…