A Piece of the Pi: mathematics explained

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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
The Parks puzzle
The Parks puzzle is a Sudoku-like game that is played on a square grid containing different coloured regions known as parks. The objective is to place…
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Richard Green
Hexagonal knot mosaics
A hexagonal knot mosaic is a way to draw a knot on a hexagonal board.
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Richard Green
7
Penny graphs
A penny graph can be created from a non-overlapping arrangement of unit circles on a flat surface.
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Richard Green
2
Ulam words and the Ulam sequence
The Ulam sequence is a sequence of positive integers xn, where x1=1, x2=2, and where each xn for n > 2 is defined to be the smallest integer that can be…
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Richard Green
5
Facially complete graphs
The Four Colour Theorem proves that no more than four colours are required to colour the regions of any map in such a way that no two adjacent regions…
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Richard Green
8
Knots and the Menger sponge
The Menger sponge is a fractal formed by iteratively subdividing a cube into 27 equal cubes, and then removing the central cube of each face and the…
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Richard Green
3
Tilings and metallic means
Two of the most famous two-dimensional models of quasicrystals are the Penrose rhomb tiling and the Ammann–Beenker tiling. Each of these types of tiling…
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Richard Green
2
Square-free words and tangrams
In mathematics, a word is a string of symbols; these symbols may be letters, numbers, or something else.
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Richard Green
7
Egyptian fractions
The ancient Egyptians had notation to represent the fraction 1/n, but not for every fraction of the form a/b. Because of this, they typically…
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Richard Green
6
Magic squares of powers
A magic square of order n is an n by n grid of integers in which each row, each column, and each of the two main diagonals adds up to the same number.
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Richard Green
Generalizations of Hofstadter’s Q-sequence
The Fibonacci numbers are the famous sequence that begins 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.
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Richard Green
7
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