历史与综述
In 2014, Paul Yiu constructed two equilateral triangles inscribed in a Kiepert hyperbola associated with a reference triangle. It was asserted that each of the equilateral triangles is triply perspective to the reference triangle, and in…
We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into six smaller triangles. We give theorems about the relationship between the radii of the circles inscribed in these triangles.
These are reminiscences of V. P. Havin (1933--2015), founder of the modern St. Petersburg analysis school.
We introduce a concept called refinement and develop two different ways of refining metrics. By applying these methods we produce several refinements of the shortest-path distance on the collaboration graph and hence a couple new versions…
In this paper we initiate some investigations on MathSciNet database. For many mathematicians this website is used on a regular basis, but surprisingly except for the information provided by MathSciNet itself, there exist almost no…
When I did my thesis defense presentation eleven years ago, I chose to present the subject of Ramsey theory from the moment calculus perspective. I don't think I did too well there (although I passed). Time has passed and this is the chance…
Some time ago Wastlund reformulated the Basel problem in terms of a physical system using the proportionality of the apparent brightness of a star to the inverse square of its distance. Inspired by this approach, we give another physical…
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The…
We give a translation from Russian into English of the article "In memory of Igor Dmitrievich Ado" written by A.V. Dorodnov and I.I. Sakhaev and published in Izv.\ Vyssh.\ Uchebn.\ Zaved.\ Mat.\ no. 8, (1984), 87--88. It is an orbituary for…
We review the well known Bertrand paradoxes, and we first maintain that they do not point to any probabilistic inconsistency, but rather to the risks incurred with a careless use of the locution "at random". We claim then that these…
At MOVES 2019, Barry Cipra casually introduced a new "Sol Lewitt" puzzle to fellow conference goers. Several brainstorming sessions ensued with Barry, Peter Winkler , Donna Dietz, and other attendees. This paper is to document the puzzle…
Although the Four Color Conjecture originated in cartography, surprisingly, there is nothing in the literature on the number of ways to color an actual geographic map with four or fewer colors. In this paper, we compute these numbers, with…
In this article we investigate some "unexpected" properties of the "Infinite Power Tower". \[y = f(x) = {x^{{x^{{x^{{x^ {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} }}}}}}}\] The…
Let $X_{t}$ denote a stationary first-order autoregressive process. Consider five contiguous observations (in time $t$) of the series (e.g., $X_{1}, ..., X_{5}$). Let $M$ denote the maximum of these. Let $\rho$ be the lag-one serial…
This paper presents a brief historical survey of iterative methods for solving linear systems of equations. The journey begins with Gauss who developed the first known method that can be termed iterative. The early 20th century saw good…
We establish some new theorems on pentagon and pentagram.
In this paper we construct a visualization of the Abel's Impossibility Theorem also known as the Abel-Ruffini Theorem. Using the canvas object in JavaScript along with the p5.js library, and given any expression that uses analytic functions…
In an analogous construction as by Euler for 4x4 matrices, a parametrization of 8x8 magic squares of squares with orthogonal rows is shown to be obtainable by extending the quaternionic method, as shown by Hurwitz, to octonions, but not…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.