Related papers: Dodecahedral bowling
The paper is proposing a short discussion on the ancient knowledge of Platonic solids, in particular, by Italic people.
Recently I have proposed the Roman Dodecahedra as ancient coincidence rangefinders. Here I discuss several data and references freely available on the Web. After analysis, the common features of these artifacts allow to tell that a Roman…
Putting several hard balls into a two-dimensional bowl can form a very basic two-dimensional model of hard-ball system. When the two-dimensional bowl has a parallel-rotation at a uniform speed around a center, when the number of balls is…
This paper provides a friendly introduction to chip-firing games and graph gonality. We use graphs coming from the five Platonic solids to illustrate different tools and techniques for studying these games, including independent sets,…
Icosahedron and dodecahedron can be dissected into tetrahedral tiles projected from 3D-facets of the Delone polytopes representing the deep and shallow holes of the root lattice D_6. The six fundamental tiles of tetrahedra of edge lengths 1…
Bronze cuboctahedral weights dated to the VIII-X centuries were found in northwest Russia near Ladoga, one of the most important trading centers in Eastern Europe in the VIII-X centuries. The history of the mathematical study of…
Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this…
Prehistoric sanctuaries of Daunia date back several thousand years. During the Neolithic and Bronze Age the farmers in that region dug hypogea and holes whose characteristics suggest a ritual use. In the present note we summarize the…
A question in geometric probability about the location of the balls in a game of bocce leads to related questions about the probability that a system of linear equations has a positive solution and the probability that a random zero-sum…
Classical billiards constitute an important class of dynamical systems. They have not only been in used in mathematical disciplines such as ergodic theory, but their properties demonstrate fundamental physical phenomena that can be observed…
We solve the game of Babylon when played with chips of two colors, giving a winning strategy for the second player in all previously unsolved cases.
We study a generalized three-dimensional stadium billiard and present strong numerical evidence that this system is completely chaotic. In this convex billiard chaos is generated by the defocusing mechanism. The construction of this…
The archimedean solids Cubus simus (snub cube) and Dodecaedron simum (snub dodecahedron) cannot be constructed by ruler and compass. We explain that for general reasons their vertices can be constructed via paper folding on the faces of a…
In the Byzantine Empire of 11-15 CE chess was played on the circular board. Two versions were known - REGULAR and SYMMETRIC. The difference between them is easy: the white queen is placed either on light (regular) or on dark square…
A system of two masses connected with a weightless rod (called dumbbell in this paper) interacting with a flat boundary is considered. The sharp bound on the number of collisions with the boundary is found using billiard techniques. In…
There is a relationship between the Borromean rings, the icosahedron and something called the Poincar\'e homology sphere. This relationship is explored in a wandering path that introduces fundamental ideas from topology and a geometric…
This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…
A novel method is proposed for moving large, pyramid construction size, stone blocks. The method is inspired by a well known introductory physics homework problem, and is implemented by tying 12 identical rods of appropriately chosen radius…
An existence of an aperiodic point for outer billiard outside regular dodecagon is proved. Additionally, almost all orbits of such an outer billiard are proved to be periodic, and all possible periods are listed explicitly. The proof is…
Recently were introduced physical billiards where a moving particle is a hard sphere rather than a point as in standard mathematical billiards. It has been shown that in the same billiard tables the physical billiards may have totally…