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

Topology 🍩

A robot that unknots knots
Imagine a robot walking a single lap of a knotted track in three dimensional space.
 • 
Richard Green
0:14
A robot that unknots knots
Imagine a robot walking one loop of a closed-circuit outdoor track.
 • 
Richard Green
5
Identifying bottlenecks in networks
A large network, such as an infrastructure network or a social network, may contain highly connected regions that are linked to each other by…
 • 
Richard Green
Constructing space-filling curves
A curve that reaches every point in the unit square is known as a space-filling curve. One of the most famous space-filling curves is the Hilbert curve…
 • 
Richard Green
3
Hexagonal knot mosaics
A hexagonal knot mosaic is a way to draw a knot on a hexagonal board.
 • 
Richard Green
7
Knots and the Menger sponge
The Menger sponge is a fractal formed by iteratively subdividing a cube into 27 equal cubes, and then removing the central cube of each face and the…
 • 
Richard Green
3
Toroidal Hitomezashi patterns
Hitomezashi is a traditional form of Japanese embroidery in which patterns arise from the alignment of single stitches made on a grid, as in the picture…
 • 
Richard Green
4
The horned sphere and the game of Hex
This picture shows the Alexander horned sphere, which is a very nonstandard way to embed a sphere into 3-dimensional space. The horned sphere, which was…
 • 
Richard Green
4
Ham sandwiches and necklace splitting
At any given time, there are two diametrically opposite points on the earth’s surface that have the same temperature and the same barometric pressure.
 • 
Richard Green
4
Fractal squares
This animation shows the construction of the Sierpiński carpet, a fractal that was first described by Wacław Sierpiński in 1916.
 • 
Richard Green
4
Prime knots and knot mosaics
A knot in mathematics refers to an embedding of a circle in three dimensional Euclidean space. Knots can be thought of as closed loops of string, and…
 • 
Richard Green
4
© 2025 A Piece of the Pi
Privacy ∙ Terms ∙ Collection notice
Start writingGet the app
Substack is the home for great culture