Related papers: Zur Irrationalit\"at in der Schule
The centuries-long practice of the teaching turned mechanics into an academic construct detached from its underlying science, the physics of macroscopic bodies. In particular, the regularities that delineate the scope of validity of…
An Engel series is a sum of reciprocals of a non-decreasing sequence $(x_n)$ of positive integers, which is such that each term is divisible by the previous one, and a Pierce series is an alternating sum of the reciprocals of a sequence…
Permutations that avoid given patterns have been studied in great depth for their connections to other fields of mathematics, computer science, and biology. From a combinatorial perspective, permutation patterns have served as a unifying…
In their recent preprint arXiv:2101.08308, Robert Dougherty-Bliss, Christoph Koutschan and Doron Zeilberger come up with a powerful strategy to prove the irrationality, in a quantitative form, of some numbers that are given as multiple…
The square root of Not is a logical operator of importance in quantum computing theory and of interest as a mathematical object in its own right. In physics, it is a square complex matrix of dimension 2. In the present work it is a complex…
A real number is called simply normal to base $b$ if every digit $0,1,\ldots ,b-1$ should appear in its $b$-adic expansion with the same frequency $1/b$. A real number is called normal to base $b$ if it is simply normal to every base $b,…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
We provide a simple way of searching for formulas of the Bailey--Borwein--Plouffe type together with an algorithm and an implementation in \texttt{sage}. Aside from rediscovering some already known formulas, the method has been used in the…
A systematic study of the trigonometric equation A tan a + B sin b = C, where A, B and C^2 are rational numbers. The special case tan Pi/11 + 4 sin 3 Pi/11 = sqrt[11] appears in the classical literature.
Statistical thinking partially depends upon an iterative process by which essential features of a problem setting are identified and mapped onto an abstract model or archetype, and then translated back into the context of the original…
Science and mathematics help people to better understand world, eliminating many inconsistencies, fallacies and misconceptions. One of such misconceptions is related to arithmetic of natural numbers, which is extremely important both for…
This is a detailed write-up of Koll\'ar's course at the EMS summer school in Algebraic Geometry in Eger, Hungary, August 1996. The topics include definitions and examples of rational and unirational varieties, with special attention to…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
We write out relations between the base of natural logarithms ($e$), the ratio of the circumference of a circle to its diameter ($\pi$), the golden ratios ($\Phi_p$) of the additive $p$-sequences, and the ratio of the diagonal of a square…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…
According to a popular belief, the decimal digits of mathematical constants such as {\pi} behave like statistically independent random variables, each taking the values 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 with equal probability of 1/10. If…
The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…
It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case…
By employing certain extended classical summation theorems, several surprising \pi and other formulae are displayed.