历史与综述

In his \textit{Brouillon Project} on conic sections, Girard Desargues studies the notion of \textit{traversale}, which generalizes that of diameter introduced by Apollonius. One often reads that it is equivalent to the notion of…

Let $K$ be a convex pentagon in the plane and let $K_1$ be the pentagon bounded by the diagonals of $K$. It has been conjectured that the maximum of the ratio between the areas of $K_1$ and $K$ is reached when $K$ is an affine regular…

Mathematical conception of infinite quantities forms a cornerstone of many disciplines of modern mathematics --- from differential calculus to set theory. In fact, it could be argued that the most significant revolutions in mathematics in…

Daniel da Silva was a remarkable Scientist and Mathematician of the mid 19th century. Working in Portugal, isolated from the main scientific centres of the time, his investigations in pure mathematics had almost no impact. Apart from giving…

First year calculus is often taught in a way that is very burdensome to the student. Students have to memorize a diversity of processes for essentially performing the same task. However, many calculus processes can be simplified and…

This papper aims to present and demonstrate Clifford's version for a generalization of Miquel's theorem with the use of Euclidean geometry arguments only.

The purpose of this report is to describe the work done to design the modules of a SPOC (Small Private On line Course) and analyse their effects on students' learning. We proposed a methodology for evaluating this platform by combining a…

The first half of the 20th century in the history of Russian mathematics is striking with a combination of dramaticism, sometimes a tragedy, and outstanding achievements. The paper is devoted to St. Petersburg-Leningrad Mathematical School.…

Problems in optimization and geometric probability are discussed, all connected with angles subtended at an observer's eye by an object at a distance. Several of these remain unsolved.

This is a review of some of the interesting properties of the Riemann Zeta Function.

We discuss the optimal presentations of mathematical objects under well defined symbol libraries. We shall examine what light our chosen symbol libraries and syntax shed upon the objects they represent. A major part of this work will focus…

In this report we consider the set of the 16 possible convex tangrams that can be composed with the 7 so-called "Sei Shonagon Chie no Ita" (or Japanese) tans, see [10]. The set of these Japanese tans is slightly different from the…

I briefly consider the Kuhnian notion of "paradigm shifts" applied to the history of mathematics and argue that the succession and intergenerational continuity of mathematical thought was undeservedly neglected in the historical studies. To…

The poem Helen of the Nobel laureate George Seferis was inspired by the anti war play Helen of Euripides. In his poem, Seferis empathizes with the hero of the tragedy, Teucer, who opposed the involvement of The Gods in the lives of the…

We investigate the impact of mathematics on improving neighbourhood integration and perception of security. The main square of Chamilpa colony in Cuernavaca, M\'exico is take as study case. This city is featured by its precarious…

In the 16th century, Simon Stevin initiated a modern approach to decimal representation of measuring numbers, marking a transition from the discrete arithmetic practised by the Greeks to the arithmetic of the continuum taken for granted…

We discuss a recursive formula for number of spanning trees in a graph. The paper is written primary for school students.

Ren{\'e} Thom discovered several refined topological notions in the writings of Aristotle, especially the biological. More generally, he considered that some of the assertions of the Greek philosophers have a definite topological content,…

Magic squares have been well explored here on Earth [1], but there appears to have been little-to-no examination of $\textit{lunar}$ magic squares. Some kinds of magic squares exist on the moon (i.e. under lunar arithmetic) but not on Earth…

We prove the statement in the title using the connectedness of the interval in real line.