
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
 Lucas de la Paz on Selfreplication
 apgoucher on Selfreplication
 Lucas de la Paz on Selfreplication
 apgoucher on New Year’s Eve
 A Morales on 29yearold Conway conjecture settled
Monthly Archives: October 2012
Happy Hallowe’en
Feeling that Complex Projective 4Space isn’t sufficiently seasonal, I was compelled to alter the colour scheme of the banner to reflect the fact that today, the 31st October, is All Hallows’ Eve, popularly abbreviated to Hallowe’en. Anyway, I actually prefer … Continue reading
Posted in Uncategorized
Leave a comment
Fusible numbers
Quite a lot of interest originated from the following puzzle of unknown origin: Given two pieces of rope which burn in precisely 1 minute, time an interval of 45 seconds (3/4 minutes). The rope is not necessarily uniform, so you’re … Continue reading
Posted in Uncategorized
Leave a comment
MODA: Diophantine equations
Here’s the penultimate chapter of Mathematical Olympiad Dark Arts. This includes several methods of solving Diophantine equations, including Vieta jumping and the Sam CapplemanLynes Technique. Also included is an explanation of how to locate rational points on algebraic curves, up to and including elliptic … Continue reading
Posted in MODA
Leave a comment
GMT
We’re quickly approaching Ebenezer Scrooge’s favourite time of the year, Greenwich Mean Time. This brief post serves as a reminder to anyone who has forgotten about the temporal adjustment due to spending too little time in real Euclidean 3space. Of course, if … Continue reading
Posted in Uncategorized
Leave a comment
Borromean strings
We’ll begin with an intriguing set of three interlinked rings, the Borromean rings. They can’t be realised as solid circular tori, but ellipses work just fine. Here is a visualisation: If you remove any one of the three rings, the … Continue reading
Posted in Uncategorized
Leave a comment
Markov basketweaving
Shortly after publishing my third cipher, the second one (labyrinth) was solved by someone called Patrick. Gabriel had worked out the basis for solving the cipher ages ago, but didn’t actually do the necessary combination of bruteforce frequency analysis to decipher it. I’m … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 3: Chess cipher
Don’t forget that the MathsJam is today, held throughout the country and indeed the world. It is suprising that noone has yet solved the maze cipher, and only one person has managed to assemble and decipher the Jigcypher. Perhaps I … Continue reading
Posted in Ciphers
Leave a comment
MODA: Inversion
On Tuesday (23rd October) at 7:00 pm, there is a monthly MathsJam gathering. It occurs simultaneously in various areas of the country, including the Castle Inn, Cambridge. I’ve heard rumours that there is a surprise party at the event for Tom Rychlik to … Continue reading
Posted in MODA
Leave a comment
Combinatorial cake
Forgive me if there is a slight lapse in the frequency of CP4space postings. You can attribute it to me lying in the quintupleintersection of the following Venn diagram: This particular arrangement of ellipses partitioning the plane into 32 connected … Continue reading
Posted in Uncategorized
Leave a comment
Surfaces
Many natural objects can be modelled by startlingly simple equations. For instance, there is a sextic surface (degree6 polynomial equation in three variables) which resembles a heart. As such, it has been nicknamed the ‘heart surface’: Now that we’re approaching … Continue reading
Posted in Uncategorized
Leave a comment