历史与综述

In the present paper I shall reveal two circular figures hidden behind the Susa mathematical text no.3,lines 5 and 6 with my own analysis of the text.

In this note we show that in addition to two integers forming a Pythagorean triple, there also exist two irrational numbers in terms of which this Pythagorean triple can also be obtained. We also put forward a relation between these two…

A relatively common sight in graphic designs is a planar arrangement of three gears in contact. However, since neighboring gears must rotate in opposite directions, none of the gears can move. We give a non-planar, and non-frozen,…

The paper presents some new results on Z-related sets obtained by computational methods. We give a complete enumeration of all Z-related sets in $\mathbb{Z}_{N}$ for small $N$. Furthermore, we establish that there is a reasonable…

Incomputability as a mathematical notion arose from work of Alan Turing and Alonzo Church in the 1930s. Like Turing himself, it attracted less attention than it deserved beyond the confines of mathematics. Today our experiences in computer…

We use the idea of the broken stick problem (which goes back to Poincare) and calculate the corresponding probabilities for the cases in which the three broken part are: the medians in a triangle, the altitudes, radii of excircles, angle…

The subject of this paper is a variation of a blackjack game, mainly popular in some parts of Europe where it is known as einz (in German slang: one). We describe the rules of this game, indicate its main characteristics, give some…

A classical theorem of d'Alembert states that if a polynomial P(x) with real coefficients has a non-real root x=a+ib, then it also has a root x=a-ib. We give a short and elementary inductive proof that avoids any properties of the complex…

This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the conformal representation upon the disc of a…

We discuss the advantages of searchable, collaborative, language-independent databases of mathematical results, indexed by "fingerprints" of small and canonical data. Our motivating example is Neil Sloane's massively influential On-Line…

This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely the so-called revolution in rigor in infinitesimal calculus and mathematical analysis.…

Leibniz entertained various conceptions of infinitesimals, considering them sometimes as ideal things and other times as fictions. But in both cases, he compares infinitesimals favorably to imaginary roots. We agree with the majority of…

Recollections of the Austrian geometer Heinrich Brauner (in German).

This article is dedicated to the investigation of difficulties involved in the understanding of the homomorphism concept. It doesn't restrict to group-theory but on the contrary raises the issue of developing teaching strategies aiming at…

Hans Grauert died in September of 2011. This article reviews his life in mathematics and recalls some detail his major accomplishments.

This is a detailed and self-contained introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios as presented in Book V of…

There are two problems Analytical Geometry with facing anyone who studies this discipline: define the nature of the locus represented by the general equation 2do degree in two or three variables: That curve represents the plane? What…

Pasting and Reversing operations have been used successfully over the set of integer numbers, simple permutations, rings and recently over a generalized vector product. In this paper, these operations are defined from a natural way to be…

We answer the question: who first proved that $C/d$ is a constant? We argue that Archimedes proved that the ratio of the circumference of a circle to its diameter is a constant independent of the circle and that the circumference constant…