历史与综述
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense…
The right triangles represented in the Plimpton 322 data have integer sides $(a, b, d)$ with $a < b < d$, by inspecting the data we propose $b=M\,Q_{M}$ with $M,Q_{M}$ positive integers. In this way we present a new data-driven family of…
This survey will appear in Vol. VII of the Hendbook of Teichm{\"u}ller theory (European Mathematical Society Publishing House, 2020). It is a commentary on Teichm{\"u}ller's paper "Einfache Beispiele zur Wertverteilungslehre", published in…
This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.
The history of the development of the concept of complex numbers from the 16th to 19th centuries. The origin and refinement of the geometric and physical meaning of complex numbers, the emergence of vectoral analysis.
This article is a tribute to one of the most prominent Polish mathematicians Jozef Marcinkiewicz who perished 80 years ago in the Katyn' massacre. His personality and main mathematical achievements are described.
This paper provides a uniform explanation of different extensions and generalizations of the butterfly theorem based on the Desargues involution theorem.
Metastability appears when a thermodynamic system, such as supercooled water (which is liquid below freezing temperature), lands on the "wrong" side of a phase transition, and remains for a very long time in a state different from its…
In this article we present diverse experiences of Polish mathematicians (in a broad sense) who during World War I fought for freedom of their homeland or conducted their research and teaching in difficult wartime circumstances. We first…
The Compositional Integral is defined, formally constructed, and discussed. A direct generalization of Riemann's construction of the integral; it is intended as an alternative way of looking at First Order Differential Equations. This brief…
In "Quartic Coincidences and the Singular Value Decomposition" by Clifford and Lachance, Mathematics Magazine, December, 2013, it was shown that if there is a midpoint ellipse(an ellipse inscribed in a quadrilateral, $Q$, which is tangent…
Nicolas-Auguste Tissot (1824--1897) was a French mathematician and cartographer. He introduced a tool which became known among geographers under the name ``Tissot indicatrix'', and which was widely used during the first half of the…
This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.
Recently it has been discovered that on a stone tablet over 3800 years old, the Plimpton-322 table, are carved the geometric relations that exist between the sides of 15 right triangles chosen in a very special way. Due to its property as a…
We describe the evolution of a personal non-lecture active learning pedagogy developed in numerous courses at all university levels. A distinguishing feature is its tight integration of pre-class preparation, involving student…
We provide a new formulation and proof of the triangle altitudes theorem in hyperbolic plane geometry, together with an easily computed discriminant to distinguish between different basic configurations of the altitudes of such a triangle.
In a general simulation of random walking (with the angle of motion picked uniformly), it can be seen that the probability of crossing a WiFi TX-RX link is directly proportional to the per-step distance and inversely proportional to the…
An overview of the history of projective representations (= spin representations) of groups, preceded by the prehistory of studies on the theory of quaternion due to Rodrigues and Hamilton. Beginning with Schur, we cover many mathematicians…
A study of Sophie Germain's extensive manuscripts on Fermat's Last Theorem calls for a reassessment of her work in number theory. There is much in these manuscripts beyond the single theorem for Case 1 for which she is known from a…
In the number $373$ all subwords ($3$, $7$, $37$, $73$, and $373$) are prime. Similarly, in $9719$ all subwords are divisible by at most one prime. And similarly again in $7319797913$ all subwords are divisible by at most two primes. These…