历史与综述
Papert's (1980) work with Turtle Geometry offered an early and provocative vision of how digital technologies could be used with young learners. Since then, research on digital technology use has focused on the middle and high school…
If a line cuts randomly two sides of a triangle, the length of the segment determined by the points of intersection is also random. The object of this study, applied to a particular case, is to calculate the probability that the length of…
Leonhard Euler was working for the St. Petersburg Academy of Sciences (Russia) and Prussian Academy of Sciences during various periods of his life. It is not a popular knowledge about Euler's contacts with Polish scientists of his era and…
In recreational mathematics, a normal magic square is an $n \times n$ square matrix whose entries are distinctly the integers $1 \ldots n^2$, such that each row, column, and major and minor traces sum to one constant $\mu$. It has been…
The aim of the talk is to trace how and when Henri Poincar\'e used non-Euclidean geometries (NEG) in his mathematical and philosophical works, with a particular attention to the genesis and the description of his model. We begin by a short…
For a long time it has been known that in the 16th century the Swiss mathematician Jost B\"urgi found a new method for calculating sines, but no information about the details has been available. Recently a manuscript written by B\"urgi…
In the first article in the series examining mathematics on coins, we discuss two great scientists who are not only featured on many coins, but also contributed to both theory and practice of coinage. The first one is Nicolaus Copernicus,…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
Rubik's Revenge, a 4x4x4 variant of the Rubik's puzzles, remains to date as an unsolved puzzle. That is to say, we do not have a method or successful categorization to optimally solve every one of its approximately $7.401 \times 10^{45}$…
Traditional mathematical notation can lead to confusion. Expressions that appear to define composite functions sometimes do not. A particular example with engineering applications is studied in detail.
We collect various facts related loosely to random Gaussian quadrilaterals in the plane. For example, a side of a degenerate quadrilateral (one point inside three others) has a density that is non-Rayleigh.
This paper offers a glimpse of the major contributions made by Arabs to mathematics in middle ages history period. Its purpose is to stimulate interest in an object based on mutual respect and understanding. We give a short list of the most…
We know that a continuous function on a closed interval satisfies the Intermediate Value Property. Likewise, the derivative function of a differentiable function on a closed interval satisfies the IVP property which is known as the Darboux…
The existence of "Hot Hands" and "Streaks" in sports and gambling is hotly debated, but there is no uncertainty about the recent batting-average of the New York Times: it is now two-for-two in mangling and misunderstanding elementary…
In 1857 Sylvester stated a result on determinants without proof that was recognized as important over the subsequent century. Thus it was a surprise to Akritas, Akritas and Malaschonok when they found only one English proof - given by…
The inverse problem of Galois Theory was developed in the early 1800 s as an approach to understand polynomials and their roots. The inverse Galois problem states whether any finite group can be realized as a Galois group over Q (field of…
We consider generalizations of a well known elementary problem. A wire of the fixed length is cut into two pieces, one piece is bent into a circle and the second one into a square. What dimensions of the circle and the square will minimize…
We discuss coin-weighing problems with a new type of coin: a chameleon. A chameleon coin can mimic a fake or a real coin, and it can choose which coin to mimic for each weighing independently. We consider a mix of $N$ coins that include…
The Maya were known for their astronomical proficiency. This is demonstrated in the Mayan codices where ritual practices were related to astronomical events/predictions. Whereas Mayan mathematics were based on a vigesimal system, they used…
This is an Open Access textbook on non-cooperative Game Theory with 165 solved exercises.