历史与综述
During his life Weyl approached the problem of space (PoS) from various sides. Two aspects stand out as permanent features of his different approaches: the {\em unique determination of an affine connection} (i.e., without torsion in the…
In this manuscript, I introduce and describe the work of mathematicians and mathematics educators in the group Transforming Post-Secondary Education in Mathematics (TPSE Math or TPSE, pronounced "tipsy", for short). TPSE aims to coordinate…
B\'ezout's name is attached to his famous theorem. B\'ezout's Theorem states that the degree of the eliminand of a system a $n$ algebraic equations in $n$ unknowns, when each of the equations is generic of its degree, is the product of the…
A catalogue of African Doctorates in Mathematics has been compiled and published in 2007 by the late Professor Paulus Gerdes. In this paper, we revise and update the list of mathematicians from Burkina-Faso. Starting from a short…
We report on the works of Euler and Chebyshev on the drawing of geographical maps. We point out relations with questions about the fitting of garments that were studied by Chebyshev.
We discuss variations of the zero-sum game where Bob selects two distinct numbers, and Alice learns one of them to make a guess which of the numbers is the larger.
We study Saccheri`s three hypotheses on a two right-angled isosceles quadrilateral, with a rectilinear summit side. We claim that in the Hilbert`s foundation of geometry the euclidean parallelism is a theorem, and in the h-plane the…
In this short, chatty paper, I describe how my attempt to use mathematics to create a 3D print of a school portrait led me a group of early 20th century French artists known as the Fauves.
It may seem a funny notion to write about theorems as old and rehashed as Descartes's rule of signs, De Gua's rule or Budan's. Admittedly, these theorems were proved numerous times over the centuries. However, despite the popularity of…
In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra, geometry and number theory
The formula for the dihedral angle of the simplex of n dimensions, arccos(1/n), is derived using classical geometry.
A simple and self-contained proof is presented of the well-known fact that the fundamental group of SO(3) is $Z_2$, using a relationship between closed paths in SO(3) and braids.
Motivated by intuitive properties of physical quantities, the notion of a non-anomalous semigroup is formulated. These are totally ordered semigroups where there are no `infinitesimally close' elements. The real numbers are then defined as…
We describe an algebraic proof of the well-known topological fact that $\pi_1(SO(n)) \cong Z/2Z$. The fundamental group of $SO(n)$ appears in our approach as the center of a certain finite group defined by generators and relations. The…
In 1866, Charles Ludwidge Dodgson published a paper concerning a method for evaluating determinants called the condensation method. His paper documented a new method to calculate determinants that was based on Jacobi's Theorem. The…
The content of this paper is the noted transcription of 84 letters that Thomas Archer Hirst wrote to Luigi Cremona and of 2 letters that Cremona wrote to Hirst between 1865 and 1892. The correspondence is stored at the Istituto Mazziniano,…
In this paper we consider a few Calculus optimization problems in which we notice peculiar patterns. In each of these cases there is a geometric explanation for the pattern showing that it is not just a coincidence.
My thesis describes the life and work of the mathematician Major Percy Alexander MacMahon (1854-1929). His early life as as a soldier in the Royal Artillery and the events which led to him embarking on a career in mathematical research and…
In a recent work, Dancs and He found new `Euler-type' formulas for $\,\ln{2}\,$ and $\,\zeta{(2\,n+1)}$, $\,n\,$ being a positive integer, each containing a series that apparently can not be evaluated in closed form, distinctly from…
This paper shows an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima and the Binomial Formula, that avoids: any root extraction other than the one used to define the modulus…