A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained

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Combinatorics 🧮

Counting dimer tilings
A dimer is a 2×1 domino-shaped rectangle.
 • 
Richard Green
2
The maximum number of SETs for 12 cards
SET is a card game that is played with a deck of 81 cards.
 • 
Richard Green
Identifying bottlenecks in networks
A large network, such as an infrastructure network or a social network, may contain highly connected regions that are linked to each other by…
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Richard Green
Constructing space-filling curves
A curve that reaches every point in the unit square is known as a space-filling curve. One of the most famous space-filling curves is the Hilbert curve…
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Richard Green
3
Chess and the number e
The number e=2.718281828459045… is one of the most famous irrational numbers.
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Richard Green
4
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.
 • 
Richard Green
2
Misère Connect Four
It is well known that it is impossible to win at noughts and crosses (tic-tac-toe) unless your opponent makes a mistake, because if both players play…
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Richard Green
3
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…
 • 
Richard Green
5
How many triangles are there?
A well-known type of brain teaser invites the reader to count the number of triangles formed by dividing up a larger triangle using straight lines.
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Richard Green
3
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…
 • 
Richard Green
8
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