A Piece of the Pi: mathematics explained

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Arranging queens on a chessboard
What is the minimum number of chess pieces of a given type needed to attack every vacant square of the board? The answer turns out to be 9 for kings, 5…
 • 
Richard Green
1
Friezes and Catalan numbers
A Conway–Coxeter frieze is an infinitely wide checkerboard of positive integers, such as the one in the picture above. Conway–Coxeter friezes were…
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Richard Green
The arithmetic derivative
Can you differentiate a number and get a nonzero answer? You can't with the usual kind of differentiation, but you can with the “arithmetic derivative…
 • 
Richard Green
The Hadwiger–Nelson problem
What is the minimum number of colours needed to colour the plane in such a way that any two points that are at distance 1 from each other always have…
 • 
Richard Green
2
Friedman numbers
A Friedman number is a positive integer that can be written (nontrivially) using its own digits, together with parentheses and the operations of…
 • 
Richard Green
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How to build a computer using origami
 • Richard Green
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Curves and L-systems
 • Richard Green
5
Diophantine m-tuples
 • Richard Green
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105 trillion digits of pi
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Friedman numbers
A Friedman number is a positive integer that can be written (nontrivially) using its own digits, together with parentheses and the operations of…
 • 
Richard Green
105 trillion digits of pi
The number π (3.1415926…) has now been computed to 105 trillion decimal places! The computational background behind this feat is discussed by Jordan…
 • 
Richard Green
The infinite monkey theorem
The infinite monkey theorem is the observation that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will…
 • 
Richard Green
3
Corridor numbers, Fibonacci numbers, and Pascal’s triangle
The corridor numbers count the number of ways one can take n diagonal steps down a corridor of fixed width, starting in the corner. The picture above…
 • 
Richard Green
Generalizations of Euler’s Tonnetz
The picture above by Konstanze Rietsch shows a Tonnetz of type G2. This is an infinite tessellation of 30°–60°–90° triangles whose edges are labelled by…
 • 
Richard Green
Top posts
How to build a computer using origami
 • Richard Green
1
Curves and L-systems
 • Richard Green
5
Diophantine m-tuples
 • Richard Green
1
105 trillion digits of pi
 • Richard Green
Fractional Sudoku
 • Richard Green
A Piece of the Pi: mathematics explained
A Piece of the Pi: mathematics explained
For the intelligent general reader who likes mathematics.
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