
Recent Posts
Subscribe to Complex Projective 4Space
Archives
 February 2021
 January 2021
 December 2020
 November 2020
 October 2020
 September 2020
 August 2020
 July 2020
 June 2020
 May 2020
 June 2019
 May 2019
 March 2019
 November 2018
 September 2018
 July 2018
 June 2018
 May 2018
 April 2018
 March 2018
 February 2018
 November 2017
 October 2017
 November 2016
 May 2016
 March 2016
 February 2016
 December 2015
 September 2015
 March 2015
 February 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
Recent Comments
 Exa on The neural network of the Stockfish chess engine
 Paul on The neural network of the Stockfish chess engine
 Beren on Outer automorphism of S6
 A curious construction of the Mathieu group M11  Complex Projective 4Space on Stella octangula
 A curious construction of the Mathieu group M11  Complex Projective 4Space on Subsumptions of regular polytopes
Monthly Archives: February 2013
Radical Tauism
Consider the Gaussian function . This gives the standard normal distribution, which has zero mean, unit variance, and points of inflection located at ±1. Note the scaling term , which is included so that the integral is 1 (necessary for a … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 18: Enigma
This was, as suggested by the title, inspired by the Enigma machine used to encode runofthemill messages during the Second World War (more highsecurity messages were encoded with the Lorenz cipher). The Enigma machine was relatively easy to operate, and … Continue reading
Posted in Ciphers
Leave a comment
27 lines on a cubic
Some of you may have noticed a particularly queer post on cp4space yesterday (since deleted), which was written by an impostor. Specifically, I was hosting several people (including, but by no means limited to, the daughter of Kjartan Poskitt). I … Continue reading
Posted in Uncategorized
Leave a comment
The torus
The torus is a reasonably interesting object. It can be embedded in as a quartic surface bounding a doughnut, or obtained by identifying opposite edges of a square. An intermediate between these constructions is the Clifford torus, which is the … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 17: Hallucinogen
After the last cipher, Joseph Myers has overtaken Sam CapplemanLynes into first place. Will it remain this way? Only time will tell… Good luck.
Posted in Ciphers
Leave a comment
What constitutes an explicit example?
Some proofs of existence provide explicit examples. For instance, a proof of a composite Fermat number is as simple as noting that . On the other hand, some existence proofs are highly nonconstructive, and do not provide explicit examples. The … Continue reading
Posted in Uncategorized
Leave a comment
Tournament dice
In an earlier cp4space post, I presented a set of five 5sided dice. We can draw a directed graph associated with this set of dice: Each vertex represents a die. If die A beats die B with a probability greater … Continue reading
Posted in Uncategorized
Leave a comment
Magic squares of squares
In 1770, Leonhard Euler sent this particular curiosity to Joseph Lagrange. It’s a 4by4 magic square, all of whose entries are perfect squares. Martin Gardner offered a prize for finding a 3by3 magic square of squares. Lee Sallows found a … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 16: The scenic route
Cipher Tuesday has been massively successful at coinciding with special occasions. We’ve had Christmas and New Year ciphers, and now this one lands on Shrove Tuesday (on reflection, I realise that will trivially happen every year!). So, to commemorate a rather exciting … Continue reading
Posted in Ciphers
Leave a comment
BMO2 marked
A group* of twelve of us congregated in London to mark† the second round of the British Mathematical Olympiad. After several hours of marking, punctuated with a surprisingly highquality lunch, we were able to announce the scores. The high scores are available on the BMOC website; well done … Continue reading
Posted in Uncategorized
Leave a comment