A Piece of the Pi: mathematics explained
Subscribe
Sign in
Home
Podcast
Notes
Chat
Advanced
Beginner
Bonus Content ➕
Browse By Topic
Archive
About
Latest
Top
Discussions
Partitions and primes
The picture above shows all the partitions of the numbers 1 up to 8. For example, the partitions of 4 are the sequences of weakly decreasing positive…
6 hrs ago
•
Richard Green
2
Share this post
Partitions and primes
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
Continued fractions
A continued fraction is an expression obtained by representing a number as the sum of its integer part and the reciprocal of another number, and then…
May 13
•
Richard Green
4
Share this post
Continued fractions
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
5
Arranging queens on a chessboard
What is the minimum number of chess pieces of a given type needed to attack every vacant square of the board? The answer turns out to be 9 for kings, 5…
May 5
•
Richard Green
5
Share this post
Arranging queens on a chessboard
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
3
April 2024
Friezes and Catalan numbers
A Conway–Coxeter frieze is an infinitely wide checkerboard of positive integers, such as the one in the picture above. Conway–Coxeter friezes were…
Apr 29
•
Richard Green
4
Share this post
Friezes and Catalan numbers
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
The arithmetic derivative
Can you differentiate a number and get a nonzero answer? You can't with the usual kind of differentiation, but you can with the “arithmetic derivative…
Apr 21
•
Richard Green
6
Share this post
The arithmetic derivative
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
The Hadwiger–Nelson problem
What is the minimum number of colours needed to colour the plane in such a way that any two points that are at distance 1 from each other always have…
Apr 15
•
Richard Green
3
Share this post
The Hadwiger–Nelson problem
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
2
Friedman numbers
A Friedman number is a positive integer that can be written (nontrivially) using its own digits, together with parentheses and the operations of…
Apr 8
•
Richard Green
9
Share this post
Friedman numbers
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
Lozenges and Löschian numbers
These pictures come from the recent paper A lozenge triangulation of the plane with integers by Raghavendra N. Bhat, Cristian Cobeli, and Alexandru…
Apr 1
•
Richard Green
6
Share this post
Lozenges and Löschian numbers
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
March 2024
PackIt! (a rectangle packing game)
The picture above comes from the recent paper PackIt! Gamified Rectangle Packing by Thomas Garrison, Marijn J.H. Heule, and Bernardo Subercaseaux…
Mar 24
•
Richard Green
7
Share this post
PackIt! (a rectangle packing game)
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
105 trillion digits of pi
The number π (3.1415926…) has now been computed to 105 trillion decimal places! The computational background behind this feat is discussed by Jordan…
Mar 15
•
Richard Green
11
Share this post
105 trillion digits of pi
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
The infinite monkey theorem
The infinite monkey theorem is the observation that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will…
Mar 11
•
Richard Green
4
Share this post
The infinite monkey theorem
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
3
Picturing symmetry
The picture above by Matthew Macauley shows the multiplication table (or Cayley table) of the symmetries of a square. The symmetries themselves are…
Mar 4
•
Richard Green
4
Share this post
Picturing symmetry
apieceofthepi.substack.com
Copy link
Facebook
Email
Note
Other
Share
Copy link
Facebook
Email
Note
Other
This site requires JavaScript to run correctly. Please
turn on JavaScript
or unblock scripts