A Piece of the Pi: mathematics explained

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

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December 2025

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

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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

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November 2025

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

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October 2025

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

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How many cylinders can touch each other?

In 1968, J.E.

Oct 13, 2025 • Richard Green

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September 2025

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

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Matroid bingo

Matroid bingo is a simplified version of the game of bingo.

Sep 15, 2025 • Richard Green

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Transparent rectangle visibility graphs

A graph consists of a set of vertices, some of which are joined in pairs by edges.

Sep 1, 2025 • Richard Green

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August 2025

Balanced Steinhaus triangles

A familiar fact from the game of pool is that 15 objects can be arranged in an equilateral triangle of side length 5.

Aug 16, 2025 • Richard Green

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How to make hyperbolic wallpaper

Given a repeating wallpaper pattern in the Euclidean plane, is there a good algorithm to turn it into a wallpaper pattern in the hyperbolic plane, as in…

Aug 6, 2025 • Richard Green

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July 2025

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

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