Related papers: Sagan numbers
In the early part of the paper, various geometrical formulas are derived. Then, at some point in the paper, the concept of a Pythagorean rational is introduced. A Pythagorean rational is a rational number which is the ratio of two integers…
Numbers are often used to define more complicated numbers. For example, two integers are used to define a rational number and two reals are used to define a complex number. It might be expected that an irrational power of an irrational…
Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.
The notion of Hausdorff number of a topological space is first introduced in \cite{bonan}, with the main objective of using this notion to obtain generalizations of some known bounds for cardinality of topological spaces. Here we consider…
We develop new aspects of the the of numerosity theory; more exactly, we emphasize its relation with the ordinal numbers, cardinal numbers, hyperreal numbers and surreal numbers. In particular, we combine the notion of numerosity with the…
In a fascinating recent American Mathematical Monthly article, Norman Wildberger and Dean Rubine introduced a new kind of combinatorial numbers, that they aptly named the ``Geode numbers''. While their definition is simple, these numbers…
We discuss the problem of galaxy correlations by considering the various methods by which this information can be obtained. We focus in particular on the volume limited three dimensional samples and discuss a new way to increase the scale…
After six decades of studying radio galaxies, we are now being delightfully overwhelmed by their exponentially expanding numbers, and the complexity of their structures. Similarly, the ways we classify radio galaxies have exploded, often…
In 1693, Isaac Newton answered a query from Samuel Pepys about a problem involving dice. Newton's analysis is discussed and attention is drawn to an error he made.
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
To represent positive integers by regular patterns on a plane or in three-dimensional space may be traced back to the Pythagoreans. The aim of the present article is to explore the possibility of extending the representation framework for…
A number $N$ is a triangular number if it can be written as $N = t(t + 1)/2$ for some nonnegative integer number $t$. A triangular number $N$ is called square if it is a perfect square, that is, $N = d^2$ for some integer number $d$. Square…
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense…
Quantitative linguistics has been allowed, in the last few decades, within the admittedly blurry boundaries of the field of complex systems. A growing host of applied mathematicians and statistical physicists devote their efforts to…
Despite the fact that almost all real numbers are absolutely normal---that is, the digits in their expansions to any base occur in all possible configurations with the expected frequency---not one specific example of an absolutely normal…
Markov numbers are integers that appear in triples which are solutions of a Diophantine equation, the so-called Markov cubic $$x^2 + y^2 + z^2 - 3x y z = 0.$$ A classical topic in number theory, these numbers are related to many areas of…
In 1882 J.J. Sylvester already proved, that the number of different ways to partition a positive integer into consecutive positive integers exactly equals the number of odd divisors of that integer (see [1]). We will now develop an…
Let n_g denote the number of numerical semigroups of genus g. Bras-Amoros conjectured that n_g possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree.…
During the voyages that led him to discover the new continent bearing his name, Amerigo Vespucci made interesting astronomical observations of the southern sky. In the past, his data have been interpreted with criteria that do not follow…
The notion of $\theta$-congruent numbers generalizes the classical congruent number problem. Recall that a positive integer $n$ is $\theta$-congruent if it is the area of a rational triangle with an angle $\theta$ whose cosine is rational.…