Related papers: Descartes-Newton-Young rainbow
We describe in detail an advanced project devised for outstanding High School (or undergraduate) students with appropriate abilities in physical reasoning (rather than with a good standard preparation), centered around the well-known…
Rainbows are generally considered to be caused by static refraction and reflection. A primary and a secondary rainbow appear due to refraction and internal reflection in a raindrop as explained by Newton. The quantum nuclear rainbow, which…
A rainbow is a captivating natural phenomenon resulting from the refraction, dispersion, and reflection of sunlight within water droplets. Traditional classroom demonstrations often focus on qualitative explanations of the formation of…
This chapter represents an attempt to summarize some of the direct and indirect connections that exist between ray theory, wave theory and potential scattering theory. Such connections have been noted in the past, and have been exploited to…
We develop a theory of multiplicities of roots for polynomials over hyperfields and use this to provide a unified and conceptual proof of both Descartes' rule of signs and Newton's "polygon rule".
The concept of rainbow connection was introduced by Chartrand et al. in 2008. It is fairly interesting and recently quite a lot papers have been published about it. In this survey we attempt to bring together most of the results and papers…
An edge-coloured graph $G$ is {\it rainbow connected} if any two vertices are connected by a path whose edges have distinct colours. This concept was introduced by Chartrand et al. in \cite{ch01}, and it was extended to oriented graphs by…
In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.
The discovery of atomic nucleus by E. Rutherford, at the beginning of the twentieth century, was the Nuclear Physics original landmark. From then, a series of experiments in which beams of particles composed of neutrons, protons and others,…
This paper is a very brief introduction to knot theory. It describes knot coloring by quandles, the fundamental group of a knot complement, and handle-decompositions of knot complements.
A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colours. The study of rainbow decompositions has a long history, going back to the work of Euler on Latin squares. In this paper we discuss…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
Here I am proposing a translation and discussion of the De Colore, one of the short scientific treatises written by Robert Grosseteste. In this very short treatise of the mid-1220s, Grosseteste continued the discussion on light and colours…
Dans ce colloque je discute la notion d'espace selon Descartes et Leibniz et j'y oppose le point de vue de Samuel Clarke et Isaac Newton comme solution pour comprendre la r\'ealit\'e du monde physique
An exact r-coloring of a set $S$ is a surjective function $c:S \rightarrow \{1, 2, \ldots,r\}$. A rainbow solution to an equation over $S$ is a solution such that all components are a different color. We prove that every 3-coloring of…
De Broglie's original idea that a photon is composed of a neutrino-antineutrino pair bound by some interaction was severely modified by Jordan. Although Jordan addressed an important problem (photon statistics) that de Broglie had not…
We compare the strength of polychromatic and monochromatic Ramsey theory in several set-theoretic domains. We show that the rainbow Ramsey theorem does not follow from ZF, nor does the rainbow Ramsey theorem imply Ramsey's theorem over ZF.…
Rainbows and boat wakes may seem unrelated, but they share deep mathematical connections through ray folding, caustics, and Airy interference. This paper explores these principles, which are also relevant for explaining phenomena such as…
Let $G$ be an edge-colored graph. The color degree of a vertex $v$ of $G$, is defined as the number of colors of the edges incident to $v$. The color number of $G$ is defined as the number of colors of the edges in $G$. A rainbow triangle…
Given an edge-coloured graph, we say that a subgraph is rainbow if all of its edges have different colours. Let $\operatorname{ex}(n,H,$rainbow-$F)$ denote the maximal number of copies of $H$ that a properly edge-coloured graph on $n$…