A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained

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Tournaments and dice games
The picture above shows a set of seven dice designed by Oskar van Deventer. An arrow between die x and die y indicates that if the dice x and y are…
 • Richard Green
“Lights Out” on a triangular grid
Lights Out is a game that can be played on an equilateral triangular grid of buttons, each of which may be in a lit or unlit state.
 • Richard Green
Surfaces and sequence graphs
The golden ratio, φ=(1+√5)/2, is a famous example of an irrational number, which means that it cannot be expressed exactly as a ratio of two integers.
 • Richard Green
The poetry of Steiner systems
A Steiner triple system consists of a set S (such as the set of seven letters {A, E, H, R, T, W, Y}) together with a set of 3-element subsets of S…
 • Richard Green
How many cylinders can touch each other?
In 1968, J.E.
 • Richard Green
Matroid bingo
Matroid bingo is a simplified version of the game of bingo.
 • Richard Green
Transparent rectangle visibility graphs
A graph consists of a set of vertices, some of which are joined in pairs by edges.
 • Richard Green
Balanced Steinhaus triangles
A familiar fact from the game of pool is that 15 objects can be arranged in an equilateral triangle of side length 5.
 • Richard Green
How to make hyperbolic wallpaper
Given a repeating wallpaper pattern in the Euclidean plane, is there a good algorithm to turn it into a wallpaper pattern in the hyperbolic plane, as in…
 • Richard Green
The binary sphere packing problem
What is the densest way to fill space with spheres of the same size?
 • Richard Green
Games in projective space
Projective geometry is a version of geometry in which there are points, lines, and planes, but in which there are no such things as distance or parallel…
 • Richard Green
Intersections of chords of a circle
The picture above shows a regular polygon with 15 vertices, including all the diagonals between the 15 vertices, and all the intersections between the…
 • Richard Green
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