Related papers: An Etruscan Dodecahedron
A brief essay on how studying neutrinos can help us to better understand the Universe.
This article proposes a fresh and direct reading of foundational texts of philosophy and aims at bringing back the inflamed debates that are contemporaneous with the birth of Greek axiomatics, and indeed at understanding what is timeless in…
These informal notes deal with some topics related to analysis on metric spaces.
Just a decade ago, only a handful of laboratories were engaged in the preparation and characterization of cosmic dust analogues and in the study of the formation of molecules on their surfaces. Now more than three dozen laboratories work on…
A polyhedron $\textbf{P} \subset \mathbb{R}^3$ has Rupert's property if a hole can be cut into it, such that a copy of $\textbf{P}$ can pass through this hole. There are several works investigating this property for some specific polyhedra:…
We present here an elementary construction of an aperiodic tile set. Although there already exist dozens of examples of aperiodic tile sets we believe this construction introduces an approach that is different enough to be interesting and…
This paper focuses on the dynamics of the eight tridimensional principal slices of the tricomplex Mandelbrot set: the Tetrabrot, the Arrowheadbrot, the Mousebrot, the Turtlebrot, the Hourglassbrot, the Metabrot, the Airbrot (octahedron) and…
Museum curators and archaeologists use analytical science to provide important information on artworks and objects. For example, scientific techniques provide information on artwork elemental composition, origin and authenticity, and…
This is a philosophy-intense physics article, or, if you wish, a physics-intense philosophy article. Also, being a mathematician, I tend to view the physics, in particular the essence of quantum physics, in emphasizing the mathematical…
Dense packings have served as useful models of the structure of liquid, glassy and crystal states of matter, granular media, heterogeneous materials, and biological systems. Probing the symmetries and other mathematical properties of the…
Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connected with magnets that can be used to introduce topics like…
In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nonstandard Analysis.
Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer…
Classical results on aperiodic tilings are rather complicated and not widely understood. Below, an alternative approach is discussed in hope to provide additional intuition not apparent in classical works.
In the analysis of three-dimensional biological microstructures such as organoids, microscopy frequently yields two-dimensional optical sections without access to their orientation. Motivated by the question of whether such random planar…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Hadronic decays and transitions are a key ingredient of hadronic physics. I discuss how hadronic decays can be explored in lattice gauge theory and review studies undertaken. I also discuss the impact of decays on masses and how lattice…
The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…
In a first article (referred here as B-O), we studied the first part of the so-called 'mathematical part' of Plato's Theaetetus, i.e. Theodorus' lesson. In the present one, we consider the sequel and the end of the passage (147d7-148b2), as…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…