历史与综述
In this paper we reformulate Miquel-Steiner's theorem and we obtain Miquel-Steiner's point locus for an arbitrary triangle. We prove that this locus is related to conjugate circles and Brocard's circle. In addition, we obtain…
This paper is concerned with the history of Rosenbrock-Wanner methods first initiated by Rosenbrock in 1963. His original ideas are highlighted and the main developments over 56 years are reviewed.
This is a book on elementary mathematics suitable to use in courses for first-year students of science and engineering. Students often find the formal approach to math courses rather discouraging, and demand 'rel-life applications' in order…
Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article…
The problem of the construction of magic squares occupied many mathematicians of the 17th century. The Polish Jesuit and polymath Adam Adamandy Kocha\'nski studied this subject too, and in 1686 he published a paper in Acta Eruditorum titled…
The Fields Medal, often referred as the Nobel Prize of mathematics, is awarded to no more than four mathematician under the age of 40, every four years. In recent years, its conferral has come under scrutiny of math historians, for…
This is a summary and verification of an elementary note written by John Blissard in 1862 for the Messenger of Mathematics. A general method of discovering trigonometric series having a closed-form sum is explained and illustrated with…
Diagonalizing a matrix $A$, that is finding two matrices $P$ and $D$ such that $A = PDP^{-1}$ with $D$ being a diagonal matrix needs two steps: first find the eigenvalues and then find the corresponding eigenvectors. We show that we do not…
These notes describe some results on dice comparisons when changing the numbers on the faces while the sum of all the face stay the same.
This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation…
Problem 1325 from the journal Crux Mathematicorum is revisited, and a new solution is presented.
A chain is an ordering of the integers 1 to n such that adjacent pairs have sums of a particular form, such as squares, cubes, triangular numbers, pentagonal numbers, or Fibonacci numbers. For example 4 1 2 3 5 form a Fibonacci chain while…
The article explores a simple yet interesting geometric problem: how to fold a notebook page so it is the most visible when the notebook is closed (i.e., as a bookmark). We start with a square page, then proceed to the rectangular page.…
The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom…
IWIMS (WWW Interactive Multipurpose Server) offers interactive resources designed over the past 20 years for teaching in various subjects (particularly focusing on mathematics, but also in biology, chemistry, economics, languages, physics),…
Ordinary differential equations and boundary value problems arise in many aspects of mathematical physics. Chebyshev differential equation is one special case of the Sturm-Liouville boundary value problem. Generating function, recursive…
We compare several approaches to the history of mathematics recently proposed by Blasjo, Fraser--Schroter, Fried, and others. We argue that tools from both mathematics and history are essential for a meaningful history of the discipline. In…
19th century real analysis received a major impetus from Cauchy's work. Cauchy mentions variable quantities, limits, and infinitesimals, but the meaning he attached to these terms is not identical to their modern meaning. Some Cauchy…
We describe a method of rendering real-time scenes in Nil geometry, and use this to give an expository account of some interesting geometric phenomena. You can play around with the simulation at www.3-dimensional.space/nil.html.
This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on 3-dimensional.space/sol.html