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

Spiral Sudoku
Suppose we have a 5×5 grid with 15 circled positions in a spiral shape as shown above.
 • 
Richard Green
5
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
4
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
2
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
3
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
2
Repunits and prime numbers
A repunit (“repeated unit”) is a number that only contains the digit 1 in some number base.
 • 
Richard Green
4
Misère Connect Four
It is well known that it is impossible to win at noughts and crosses (tic-tac-toe) unless your opponent makes a mistake, because if both players play…
 • 
Richard Green
2
How many triangles are there?
A well-known type of brain teaser invites the reader to count the number of triangles formed by dividing up a larger triangle using straight lines.
 • 
Richard Green
3
Wherever you go, I win!
In theory, the objective of chess is to capture the king, but in practice, the game ends two moves earlier in the position of checkmate. We can imagine…
 • 
Richard Green
2
Permutation Wordle
In the well-known game Wordle, a player has six attempts to guess a five-letter English word.
 • 
Richard Green
3
© 2025 A Piece of the Pi
Privacy ∙ Terms ∙ Collection notice
Start writingGet the app
Substack is the home for great culture