A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained

Home
Podcast
Notes
Chat
Advanced
Beginner
Bonus Content ➕
Browse By Topic
Archive
Leaderboard
About

Beginner Posts

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…
 • Richard Green
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.
 • Richard Green
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…
 • Richard Green
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.
 • Richard Green
Spiral Sudoku
Suppose we have a 5×5 grid with 15 circled positions in a spiral shape as shown above.
 • Richard Green
Tiling the plane with congruent polygons
It is impossible to tile the plane with regular pentagons of the same size, because the internal angle of a pentagon is 108°, and 360 is not a multiple…
 • Richard Green
Anti-inductive dice
David and Goliath each have a six-sided die.
 • Richard Green
Which way is the bike going?
Is it possible to deduce the direction of motion of a bicycle just by looking at the shape of the tracks it leaves?
 • Richard Green
Rubik’s abstract polytopes
The well-known puzzle Rubik’s Cube can be generalized in a number of ways, for example by turning it into a 4×4×4 or 5×5×5 puzzle.
 • Richard Green
Turning a triangle into a square
In 1902, Henry Dudeney showed that it is possible to cut an equilateral triangle into four polygonal pieces, and then to rotate and translate those…
 • Richard Green
Chutes, ladders, and Markov chains
The classic board game of Snakes and Ladders (or Chutes and Ladders) originated almost 2000 years ago in India, where it is known as Moksha Patam (see…
 • Richard Green
Repunits and prime numbers
A repunit (“repeated unit”) is a number that only contains the digit 1 in some number base.
 • Richard Green
© 2026 A Piece of the Pi · Privacy ∙ Terms ∙ Collection notice
Start your SubstackGet the app
Substack is the home for great culture