A Piece of the Pi: mathematics explained
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Tredoku Patterns
Tredoku is a generalization of Sudoku in which each 3×3 box forms part of the surface of a 3-dimensional stack of cubes. Like Sudoku, the goal is to…
Jul 22
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Richard Green
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The Rascal triangle
The Rascal triangle is a triangular array of numbers that is a variant of Pascal’s triangle.
Jul 15
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Richard Green
13
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The Rascal triangle
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How to solve any maze using the digits of π
Is there a universal, deterministic sequence of actions that can solve any maze, assuming that the actions are applied blindly with no sensor feedback…
Jul 8
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Richard Green
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How to solve any maze using the digits of π
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Peaceable armies of queens
The peaceable queens problem is to determine the maximum number m such that one can place m queens of each colour on an n by n chessboard without any…
Jul 1
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Richard Green
6
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Peaceable armies of queens
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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…
Jun 24
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Richard Green
11
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Egyptian fractions
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How to build a computer using origami
Sep 20, 2023
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Richard Green
18
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How to build a computer using origami
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Curves and L-systems
Nov 3, 2023
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Richard Green
16
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Curves and L-systems
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Diophantine m-tuples
Oct 13, 2023
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Richard Green
14
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Diophantine m-tuples
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105 trillion digits of pi
Mar 15
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Richard Green
11
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105 trillion digits of pi
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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…
Jun 17
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Richard Green
8
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Magic squares of powers
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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. Each term, other than the first two, is obtained by looking…
Jun 10
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Richard Green
9
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Generalizations of Hofstadter’s Q-sequence
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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…
Jun 3
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Richard Green
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Wallpaper groups and interlocking assemblies
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Conway’s look-and-say sequence in base 3
This graphic illustrates the look-and-say sequence, in which each successive term is obtained by reading out the inventory of digits in the previous…
May 27
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Richard Green
8
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Conway’s look-and-say sequence in base 3
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Partitions and primes
The picture above shows all the partitions of the numbers 1 up to 8. For example, the partitions of 4 are the sequences of weakly decreasing positive…
May 20
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Richard Green
7
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Partitions and primes
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How to build a computer using origami
Sep 20, 2023
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Richard Green
18
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How to build a computer using origami
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Curves and L-systems
Nov 3, 2023
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Richard Green
16
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Curves and L-systems
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Diophantine m-tuples
Oct 13, 2023
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Richard Green
14
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Diophantine m-tuples
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105 trillion digits of pi
Mar 15
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Richard Green
11
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105 trillion digits of pi
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Fractional Sudoku
Oct 27, 2023
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Richard Green
12
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Fractional Sudoku
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A Piece of the Pi: mathematics explained
For the intelligent general reader who likes mathematics.
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