
Recent Posts
Subscribe to Complex Projective 4Space
Archives
 January 2022
 December 2021
 September 2021
 July 2021
 June 2021
 May 2021
 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
 Luís Rato on Triangling the square
 charmvirgo on Conway polyhedron notation
 Daniel Sebald on Leech lattice
 Daniel Sebald on Spin groups
 Anonymous on Hyperbolic Minecraft
Monthly Archives: March 2013
Threedimensional chess
This is the first of a projected series of articles investigating a natural threedimensional generalisation of chess. In the first article, I’ll briefly describe the rules and mention previous research in this area. The second article will show how to create a linearbounded … Continue reading
Posted in Chess
Leave a comment
Urinals
In 2010, Evangelos Kranakis and Danny Krizanc published an academic paper with a rather bizarre title. The Urinal Problem investigates a particular mathematical model arising from the behaviour of men selecting urinals in a bathroom arrangement. Rather atypical of mathematical publications, … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 22: There be dragons
This cipher has the interesting property that any vertical, horizontal or diagonal line hits an even number of characters. Of course, this piece of useless information won’t help you in the slightest.
Posted in Ciphers
Leave a comment
Rational distance problem
Suppose we have a unit square ABCD. Is it possible to place a point P in the plane of ABCD, such that PA, PB, PC and PD are all rational? It’s not too difficult to show that such a point … Continue reading
Posted in Uncategorized
Leave a comment
Holyhedra
Euler’s formula famously relates the number of vertices, edges and faces of a polyhedron. Specifically, it gives , where V, E and F are the numbers of vertices, edges and faces, respectively. For example, the dodecahedron has 20 vertices, 30 … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 21: Sudoku
You’ll need to solve a couple of NPhard puzzles along the way. Enjoy! As usual, a password (which is entirely in lowercase) is included in the ciphertext, and allows you to access the secret area.
Posted in Ciphers
Leave a comment
Generalising Erdős’ conjecture
It’s a wellknown fact that the harmonic series (i.e. the sum of the reciprocals of the natural numbers) diverges to infinity. There are at least two reasonably straightforward ways to prove this, the first being the Cauchy condensation test. Essentially, … Continue reading
Posted in Uncategorized
Leave a comment
Three directions
Firstly, I would like to announce that today is the Ides of March. Secondly, I was alerted on two semirecent occasions to this beast of a puzzle, namely the regular expression crossword. Like a normal crossword, you populate the empty cells of a grid … Continue reading
Posted in Uncategorized
Leave a comment
Antoine’s necklace
(Sorry about the recent dearth of cp4space postings; I’ve been rather busy in real Euclidean 3space, .) Quite a large class of selfsimilar geometrical objects can be expressed as iterated function systems. For instance, the Sierpinski triangle is composed of three … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 20: Ulam
It’s difficult to believe that this is the twentieth cp4space cipher. Anyhow, here it is:
Posted in Ciphers
Leave a comment