Related papers: A Solution to Galileo's Enigma "Mostro Son Io"
Suppose that G is a discrete abelian group and A is a finite symmetric subset of G. We show two main results. i) Either there is a set H of O(log^c|A|) subgroups of G with |A \triangle \bigcup H| = o(|A|), or there is a character X on G…
Since the time of ancient civilizations, cosmology had a privileged place within the various artistic and literary manifestations. The Divine Comedy by Dante Alighieri, one of the masterpieces in literature and thought of the Western World,…
In this paper we start from the original formulation of the galileon model with the original choice for couplings to gravity. Within this framework we find that there is still a subset of possible Lagrangians that give selfaccelerating…
A new solution of Fermi's paradox sketched by SF writer Karl Schroeder in his 2002. novel "Permanence" is critically investigated. It is argued that this solution is tightly connected with adaptationism - a widely discussed working…
The major hindrance in the study of earlier scientific literature is the availability of Latin translations into modern languages. This is particular true for the works of Euler who authored about 850 manuscripts and wrote a thousand…
This is a translation from Latin of E840 'De motu cometarum in orbitis parabolicis, solem in foco habentibus', in which Euler addresses six problems related to comets in heliocentric parabolic orbits. Problem 1: Find the true anomaly of a…
A formal axiomatic mathematical framework for Boolos' Hardest Logic Puzzle Ever is presented and two theorems about its solvability are proved. By strictly following Boolos' instructions (in particular, the requirement that all gods are…
In the middle of the seventeenth century, Andr\'e Tacquet, S.J. briefly discussed a scientific argument regarding the structure of a Copernican universe, and commented on Galileo Galilei's discussion of that same argument -- Galileo's…
We consider various properties and manifestations of some sign-alternating univariate polynomials borne of right-triangular integer arrays related to certain generalizations of the Fibonacci sequence. Using a theory of the root geometry of…
The classical Apollonius' problem is to construct circles that are tangent to three given circles in a plane. This problem was posed by Apollonius of Perga in his work "Tangencies". The Sylvester problem, which was introduced by the English…
The aim of this paper is to generalize Apollonius' problem. The problem is to construct a circle that is tangent to three given circles in a plane. We find the maximum possible number of solution circles in the case of more than the three…
We study quadrilaterals inscribed and circumscribed about conics. Our research is guided by experiments in software Cinderella. We extend the known results in projective geometry of conics and show how modern mathematical software brings…
In his interviews with Eckermann in the 1820s, Goethe referred to his Theory of Colors as his greatest and ultimate achievement. Its reception following publication in 1810 and subsequent reviews throughout the history of physical science…
The rapid advancement of Generative AI has raised significant questions regarding its ability to produce creative and novel outputs. Our recent work investigates this question within the domain of chess puzzles and presents an AI system…
Classical applications of Galois theory concern algebraic numbers and algebraic functions. Still, the night before his duel, Galois wrote that his last mathematical thoughts had been directed toward applying his "theory of ambiguity to…
This is a translation from Latin of 'De novo oscillationum genere', which was motivated by Krafft's accidental observation of a suspended clock setting itself in constant motion as a pendulum. This publication, in turn, motivated Euler to…
Vector Galileons are ghost-free systems containing higher derivative interactions of vector fields. They break the vector gauge symmetry, and the dynamics of the longitudinal vector polarizations acquire a Galileon symmetry in an…
We present a conclusive answer to Bertrand's paradox, a long standing open issue in the basic physical interpretation of probability. The paradox deals with the existence of mutually inconsistent results when looking for the probability…
There are two hypotheses on Leonardo's polyhedron based on the Pseudo-RCO and drawn for Luca Pacioli's book: Leonardo made an error, or: Leonardo draw it with intention, as it is. We give arguments, which support the Intention-hypothesis.
We propose an interpretation of the cosmological constant puzzle - i.e., the enormous value of the ratio $\rho_{Pl}/\rho_{vac} \approx 10^{120} $- in terms of the total number of gravitons in the observable universe based on a recently…