Related papers: Dodecahedral bowling
The possible discovery of astronomical effects due to precession - such as the shift in the declination of heliacal raising of bright stars or the precession of the equinoxes - is reviewed for various ancient cultures in the world. Although…
In the paper we will describe three instruments of particular historical and didactic interest belonging to the Historical Collection of Physics Instruments of Palermo University: a convex mirror most likely dating back to the early…
We perform fractal analysis on a closed classical hard-wall billiard, the circular billiard with a straight cut, assuming there are two openings on the boundary. We use a two-dimensional set of initial conditions that produce all possible…
A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the…
We study the coupling of bouncing-ball modes to chaotic modes in two-dimensional billiards with two parallel boundary segments. Analytically, we predict the corresponding decay rates using the fictitious integrable system approach.…
The classical three-body problem arose in an attempt to understand the effect of the Sun on the Moon's Keplerian orbit around the Earth. It has attracted the attention of some of the best physicists and mathematicians and led to the…
This article sketches the proofs of two theorems about sphere packings in Euclidean 3-space. The first is K. Bezdek's strong dodecahedral conjecture: the surface area of every bounded Voronoi cell in a packing of balls of radius 1 is at…
The twentieth century has seen the rise of a new type of video games targeted at a mass audience of "casual" gamers. Many of these games require the player to swap items in order to form matches of three and are collectively known as…
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
We describe the construction of a new family of developable rollers based on the Platonic solids. In this way kinetic sculptures may be realised, with the Platonic solids quite literally in their heart. We also describe the strong way in…
Barred galaxies often develop a box/peanut pseudobulge, but they can also host a nearly spherical classical bulge, which is known to gain rotation due to the bar. We aim to explore how the presence of gas impacts the rotation of classical…
Bayesian mechanics is a new approach to studying the mathematics and physics of interacting stochastic processes. Here, we provide a worked example of a physical mechanics for classical objects, which derives from a simple application…
In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].
We investigate two-dimensional, periodic ornaments of the Late Hellenistic (some centuries before the Common Era, the Classical Period) and Early Roman (Common Era) classical periods found at different locations in Asia Minor in Turkey and…
The interpolation problem is a natural and fundamental question whose roots trace back to ancient Greece. The story is long and rich, with many chapters, and a complete solution has been obtained only recently. Exploring it leads us on a…
Based on Brownian ratchets, a counter-intuitive phenomenon has recently emerged -- namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the…
I present a jaunty little $[[14, 3, 3]]$ non-CSS surface code that can be described using a rhombic dodecahedron. Do with it what you will.
Pentagonal dodecahedral buckyball-like water clusters and arrays thereof are shown from first-principles electronic-structure calculations to possess unique terahertz vibrational modes in the 1-6 THz range, corresponding to…
This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…
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…