A Piece of the Pi: mathematics explained

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Abstract Algebra 𝑥

A polynomial with Rubik’s cube symmetry
Rubik’s Cube is a well-known combination puzzle that was invented by Ernő Rubik in 1974.
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Richard Green
3
Wallpaper groups and interlocking assemblies
The patterns in the picture above illustrate an example of a wallpaper group, which is a two-dimensional repeating pattern with a particular kind of…
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Richard Green
2
Picturing symmetry
The picture above by Matthew Macauley shows the multiplication table (or Cayley table) of the symmetries of a square.
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Richard Green
Pyritohedral symmetry
The mineral iron pyrite, also known as “fool’s gold”, usually forms cube-shaped crystals, but it can also form crystals like these. At first glance…
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Richard Green
The McNugget monoid
How many chicken nuggets can you buy if they are only sold in packs of 6, 9 and 20? The picture shows all the numbers from 0 to 44 that can be made from…
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Richard Green
9
Sandpiles and the Vicsek fractal
This picture shows an example of a stable configuration in the abelian sandpile model on a square lattice. This is a rectangular square array of a large…
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Richard Green
Hadamard matrices
A Hadamard matrix of order n is an n×n matrix whose entries are all +1 or –1, with the property that any two distinct rows agree in exactly half of…
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Richard Green
Automorphic numbers
An automorphic number is a number whose square ends in the digits of the number itself.
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Richard Green
The number 163
The numbers π and e are famous constants, approximately equal to 3.141592653589793... and 2.718281828459045..., respectively. Remarkably, the number e…
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Richard Green
Loaded dice and unfair polynomials
If you throw a pair of fair dice, you are six times more likely to throw a total of 7 than a total of 12. This is because the only way to throw a 12 is…
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Richard Green
5
The graphic nature of groups
Character theory is an area of abstract algebra that is closely related to group theory, the abstract study of symmetry.
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Richard Green
1
Bonus content: The graphic nature of groups
In the main post, I mentioned that the set {0, 1, 2, 3, 4, 5} under the operation of addition modulo 6 is a group.
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Richard Green
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