历史与综述

This article attempts at a linear historical and mathematical commentary of Kronecker's programmatic memoir "Grundz\"uge einer arithmetischen Theorie der algebraischen Gr\"ossen" (1882).

In this paper we propose a well-justified synthetic approach of the projective space. We define the concepts of plane and space of incidence and also the Gallucci's axiom as an axiom to our classical projective space. To this purpose we…

Real quadric curves are often referred to as "conic sections," implying that they can be realized as plane sections of circular cones. However, it seems that the details of this equivalence have been partially forgotten by the mathematical…

We briefly review some of Ramanujan's contributions to mathematics, including his $1/\pi$ series, his work on modular forms, and his work on partitions. We briefly review his life, including his collaboration with Hardy. Finally, we give a…

The Goldbach conjecture states that every even number can be decomposed as the sum of two primes. Let $D(N)$ denote the number of such prime decompositions for an even $N$. It is known that $D(N)$ can be bounded above by $$ D(N) \leq C^*…

This paper studies the minimal length representation of the natural numbers. Let O be a fixed set of integer-valued functions (primarily hyperoperations). For each n, what is the shortest way of expressing n as a combinations of functions…

We establish fun parallels between coin-weighing puzzles and knights-and-knaves puzzles.

The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality…

This short paper aims to investigate some of the historical developments of one classic, well-cited and highly esteemed scientific journal in the domain of quantitative operations research - namely the INFORMS journal Operations Research -…

We translate Erland Samuel Bring's treatise Meletemata quaedam Mathematica circa Transformationem Aequationum Alebraicarum (Some selected mathematics on the Transformation of Algebraic Equations) written as his Promotionschrift at the…

In a previous paper we defined the circumconic of a triangle $ABC$ with respect to a point $P$ as the conic $\tilde C=T_{P'}^{-1}(N_{P'})$, where $N_{P'}$ is the $9$-point conic for the quadrangle $ABCP'$ with respect to the line at…

We consider three problems about cities from Alcuin's_Propositiones ad acuendos juvenes_. These problems can be considered as the earliest packing problems difficult also for modern state-of-the-art packing algorithms. We discuss the…

We briefly recall the history of the Nijenhuis torsion of (1,1)-tensors on manifolds and of the lesser-known Haantjes torsion. We then show how the Haantjes manifolds of Magri and the symplectic-Haantjes structures of Tempesta and Tondo…

Haga's fold in paper folding is generalized. Recent generalization of Haga's theorems and problems in Wasan geometry involving Haga's fold are also generalized.

The Chinese abacus is the resource presented in this paper, to teach and learn number sense and place-value system at primary level. The Chinese abacus can be material, virtual (software) or drawn on a worksheet. We present three tasks and…

It is a story about the problem whether folding a square on the plane can increase its perimeter. The paper is written primary for school students.

In this paper we report a study in which we have developed a teaching cycle based closely on Bloom's Learning for Mastery (LFM). The teaching cycle ameliorates some of the practical problems with LFM by making use of the STACK online…

In this paper, we introduce a new generalization of Pascal's triangle. The new object is called the hyperbolic Pascal triangle since the mathematical background goes back to regular mosaics on the hyperbolic plane. We describe precisely the…

The paper is devoted to the contribution in the Probability Theory of the well-known Soviet mathematician Alexander Yakovlevich Khintchine (1894-1959). Several of his results are described, in particular those fundamental results on the…

We present the solution to a problem presented by Knuth, attributed to Gosper.