历史与综述
We provide an alternative proof that $\sqrt{2}$ is irrational that does not begin with the assumption that $\sqrt{2}$ is in fact rational.
We usually construct mathematical objects that are accessible, on which we can put our hands, but a huge part of the mathematical existing is actually wild. Here we explore part of the wild world: its inhabitants are knots that are…
We review Euler's idea on the Gammafunction. We will explain, how Euler obtained them and how Euler's ideas anticipate more modern approaches and theories. Furthermore, some questions asked by Euler are answered.
A method of obtaining the number pi is considered, which derives pi from the number of elastic collisions between two blocks and a wall.
This article discusses the life and work of Professor Ola Bratteli (1946--2015). Family, fellow students, his advisor, colleagues and coworkers review aspects of his life and his outstanding mathematical accomplishments.
Our main aim is to analyse three articles of Germ\'an Ancochea (published 1941, 1942 and 1947) and to describe their impact in algebra and geometry.
The purpose of this note is to provide a gentle introduction to basic universal algebra and (abstract) clones.
A summary of an experimental course on fractals is given that was held for young learners at age 12. The course was a part of Epsilon camp, a program designed for very gifted students who have already demonstrated high interest in studying…
This paper explores two preservice mathematics teachers' understanding of mode. Participants' initial understanding and understanding following use of an interactive virtual manipulative is examined. Findings suggest that participants…
This paper explores middle-grade students' conceptions of median. Describes, where and why they struggle and provides learning trajectory to improve their understanding.
Balancing square and rectangular tables by rotation has been a interesting way to illustrate the intermediate value theorem. The aim of this note is to show that the balancing act but with non-rectangular tables can be a nice application of…
I shall sketch the contents of Noether's 1918 article, "Invariante Variationsprobleme", in the context of the debate on the conservation of energy that had arisen from Einstein's general theory of relativity. How original was Noether's…
As a generalization of planar Fibonacci spirals that are based on the recurrence relation $F_n=F_{n-1}+F_{n-2}$, we draw assembled spirals stemming from analytic solutions of the recurrence relation $G_n=a\, G_{n-1}+b\, G_{n-2}+c\, d\,^n$,…
Fold-and-cut theorem claims the possibility to cut out from a sheet a set of straight-line drawing using only one cut of scissors, without producing any other cut in the sheet and separating all the figures at the same time, just by folding…
This article explores the parallels between improvisational theater (Improv) and teaching in an Active Learning environment. It presents the notions of Active Teaching as a natural complement to Active Learning, and discusses how unexpected…
In this survey essay, I explore the application of the discharging method in graph theory, including the selection of charging rules and discharging rules, and the general characteristics of the discharging method. As examples, I will prove…
We propose a new approach to solve the classical Monty Hall problem in its general form. The solution is based on basic tools of probability theory, by defining three elementary events which decompose the sample space into a partition. The…
This paper introduces topological data analysis. Starting from notions of a metric space and some elementary graph theory, we take example sets of data and demonstrate some of their topological properties. We discuss simplicial complexes…
This article is a collection of several memories for a special issue of SIGMA devoted to Dmitry Borisovich Fuchs.
We give an overview of several of the mathematical works of Gilles Lachaud and provide a historical context. This is interspersed with some personal anecdotes highlighting many facets of his personality.