A Piece of the Pi: mathematics explained
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Surfaces and sequence graphs
The golden ratio, φ=(1+√5)/2, is a famous example of an irrational number, which means that it cannot be expressed exactly as a ratio of two integers.
Jan 31
•
Richard Green
9
4
1
Colouring identical cuboids
How many colours do we need to colour a fixed stack of identical cuboids with integer coordinates in such a way that no two cuboids of the same colour…
Dec 30, 2025
•
Richard Green
6
2
2
Modular curve stitching
Consider the points of a clock face, numbered 1 up to 12, and for each point k, draw a straight line between k and 2k, taking remainders modulo 12.
Dec 10, 2025
•
Richard Green
11
6
4
The poetry of Steiner systems
A Steiner triple system consists of a set S (such as the set of seven letters {A, E, H, R, T, W, Y}) together with a set of 3-element subsets of S…
Nov 14, 2025
•
Richard Green
8
15
2
Perfect difference sets and Sidon sets
Consider a wheel with 21 evenly spaced positions, consecutively numbered 0, 1, 2, up to 20, and highlight the positions 1, 2, 5, 15, and 17 in bold, as…
Oct 30, 2025
•
Richard Green
7
2
2
Beginner Posts
View all
Colouring identical cuboids
How many colours do we need to colour a fixed stack of identical cuboids with integer coordinates in such a way that no two cuboids of the same colour…
Dec 30, 2025
•
Richard Green
6
2
2
Modular curve stitching
Consider the points of a clock face, numbered 1 up to 12, and for each point k, draw a straight line between k and 2k, taking remainders modulo 12.
Dec 10, 2025
•
Richard Green
11
6
4
Perfect difference sets and Sidon sets
Consider a wheel with 21 evenly spaced positions, consecutively numbered 0, 1, 2, up to 20, and highlight the positions 1, 2, 5, 15, and 17 in bold, as…
Oct 30, 2025
•
Richard Green
7
2
2
The golden ratio as a number base
The Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …) are one of the most famous sequences of integers.
Sep 27, 2025
•
Richard Green
20
8
5
Spiral Sudoku
Suppose we have a 5×5 grid with 15 circled positions in a spiral shape as shown above.
Jul 23, 2025
•
Richard Green
10
5
1
Top posts
How to build a computer using origami
Sep 20, 2023
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Richard Green
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Chess and the number e
Dec 16, 2024
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Richard Green
31
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The golden ratio as a number base
Sep 27, 2025
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Richard Green
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The geometry of musical keys
May 21, 2025
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Richard Green
27
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Curves and L-systems
Nov 3, 2023
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Richard Green
16
4
2
A Piece of the Pi: mathematics explained
For the intelligent general reader who likes mathematics.
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Combinatorics 🧮
View all
Surfaces and sequence graphs
The golden ratio, φ=(1+√5)/2, is a famous example of an irrational number, which means that it cannot be expressed exactly as a ratio of two integers.
Jan 31
•
Richard Green
9
4
1
Colouring identical cuboids
How many colours do we need to colour a fixed stack of identical cuboids with integer coordinates in such a way that no two cuboids of the same colour…
Dec 30, 2025
•
Richard Green
6
2
2
The poetry of Steiner systems
A Steiner triple system consists of a set S (such as the set of seven letters {A, E, H, R, T, W, Y}) together with a set of 3-element subsets of S…
Nov 14, 2025
•
Richard Green
8
15
2
How many cylinders can touch each other?
In 1968, J.E.
Oct 13, 2025
•
Richard Green
7
1
2
Matroid bingo
Matroid bingo is a simplified version of the game of bingo.
Sep 15, 2025
•
Richard Green
8
3
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