Related papers: A Solution to Galileo's Enigma "Mostro Son Io"
We consider the challenging problem of obtaining an analytic understanding of realistic astrophysical dynamics in the presence of a Vainshtein screened fifth force arising from infrared modifications of General Relativity. In particular, we…
Cultural heritage relating to the sky in the form of sundials, old observatories and the like, are commonly found in many cities in the Old World, but rarely in the New. This paper examines astronomical heritage embodied in the Barolo…
This is an English translation from the Latin original of Leonhard Euler's ``Solutio facilior problematis Diophantei circa triangulum, in quo rectae ex angulis latera opposita bisecantes rationaliter exprimantur''. In this paper, Euler…
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by I. Shirokov. The varieties of the deformed Galilei algebras are discussed and families of…
Finding solution values for unknowns in Boolean equations was a principal reasoning mode in the Algebra of Logic of the 19th century. Schr\"oder investigated it as Aufl\"osungsproblem (solution problem). It is closely related to the modern…
The problem of describing the free motions of three gravitating bodies under each others gravitational influence is one of the oldest of unsolved problems of classical mechanics. Henry Poincare proved in his dictum that due to the nature of…
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit…
We explore the possibility of creating of solitons in gravitating gas. It is shown that the virial arguments does not put an obstacle for the existence of localized static solutions. The simplest toroidal soliton of gravitating gas could be…
For a set $A$ of positive integers with $\gcd(A)=1$, let $\langle A \rangle$ denote the set of all finite linear combinations of elements of $A$ over the non-negative integers. Then it is well known that only finitely many positive integers…
Icosoku is a challenging and interesting puzzle that exhibits highly symmetrical and combinatorial nature. In this paper, we pose the questions derived from the puzzle, but with more difficulty and generality. In addition, we also present a…
Among the geniuses of mankind, Einstein was probably one of those who made more erroneous claims, and often changed his opinion during the years on important scientific subjects. However, it is important to bear in mind that his mistakes…
The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using numerical algebraic geometry gives information about the…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
Raffaello Caverni, a Catholic priest, was a truly lay and anti-establishment intellectual in his opinions both on Darwin and on Galileo. He opposed the mythicization of Galileo, as a rule in Italy after the unification, even though he…
The Eulerian numbers form a triangular array with many interesting properties. The numbers arise from various combinatorial and probabilistic interpretations, and have been studied in a variety of mathematical contexts. In this article we…
The modern usage of the words astronomy and astrology is traced back to distinctions, largely ignored in recent scholarship. Three interpretations of celestial phenomena (in a geometric, a substantialist and a prognostic versions) coexisted…
Sudoku grids can be thought of as graphs where the vertices are the squares of the grid, and edges join vertices in the same row, column, or sub-grid. A Sudoku puzzle corresponds to a partial proper coloring of the Sudoku graph. We provide…
In 1614, the German astronomer Simon Mayr published his claim to have discovered the satellites of Jupiter. Writing in the treatise Mundus Jovialis, Mayr made his assertion in a convoluted but unequivocal manner, earning the displeasure of…
Chameleon and similar (symmetron and dilation) theories of gravity can exhibit new and interesting features on cosmological scales whilst screening the modifications on small scales thereby satisfying solar system tests of general…
In this paper, an efficient algorithm to find the center of the biggest circle inscribed in a given polygon is described. This work was inspired by the publication of Daniel Garcia-Castellanos & Umberto Lombardo and their algorithm used to…