Related papers: An invitation to Fibonacci digits
This is neither an elementary introduction to singularity theory nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus,…
The study of decimal numbers in secondary education is often approached from algorithmic perspectives, which limits students' understanding of their structure. This paper presents the task Footprints of the Walking of Numbers, a dynamic…
This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.
These are the notes from my courses on the arithmetic of quadratic forms.
The purpose of this note is twofold: firstly to improve the known results on variation of extreme eigenvalues of birth and death matrices and random walk matrices; and secondly to progress towards the solution of a thirty years old open…
The authors investigate how teaching art and astronomy together has the potential to inspire new art forms, enhance scientific public outreach, and promote art and science education. The authors teach an astro-animation class at the…
Connections appear to be helpful in many contexts, such as obtaining a job, a promotion, a grant, a loan, or publishing a paper. This may be due either to favoritism or to information conveyed by connections. Attempts at identifying both…
Drawing on the Data and Predictions strand of the Indicazioni Nazionali per il curricolo 2012, this study proposes a problem based instructional approach to the teaching of probability. More specifically, the study adopts a design based…
This note generalizes the Fibonacci primitive roots to the set of integers. An asymptotic formula for counting the number of integers with such primitive root is introduced here.
The purpose of this article is to survey some of the context, achievements, challenges and mysteries of the field of metric dimension reduction, including new perspectives on major older results as well as recent advances.
There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…
We give a self contained introduction to numerical semigroups, and present several open problems centered on their factorization properties.
These notes deal with metric spaces, Hausdorff measures and dimensions, Lipschitz mappings, and related topics. The reader is assumed to have some familiarity with basic analysis, which is also reviewed.
These informal notes deal with Fourier series in one or more variables, Fourier transforms in one variable, and related matters.
This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.
Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
The aim of this note is to provide a natural extension of Gelfond's constant $e^\pi$ using a hypergeometric function approach. An extension is also found for the square root of this constant. A few interesting special cases are presented.
In this paper, we present a series of mathematical problems which throw interesting lights on flamenco music. More specifically, these are problems in discrete and computational mathematics suggested by an analytical (not compositional)…
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.