
Recent Posts
Subscribe to Complex Projective 4Space
Join 2,971 other subscribersArchives
 July 2024
 January 2024
 July 2023
 March 2023
 February 2023
 January 2023
 October 2022
 September 2022
 July 2022
 June 2022
 May 2022
 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
Monthly Archives: September 2012
Hiatus interruptus
I shall be rather busy during the next couple of months, so there may be a noticeable drop in the frequency of posts on Complex Projective 4Space. Nevertheless, I shall endeavour to maintain a steady stream of interesting articles, assuming I … Continue reading
Posted in Uncategorized
Leave a comment
Good fibrations
We’ll begin by considering Hamiltonian quaternions, a fourdimensional extension to the complex numbers. A particularly interesting bunch of quaternions is the multiplicative group of 120 ‘icosians’. These can be thought of as the vertices of a 600cell or, by duality, the … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 2: Labyrinth
The Labyrinth usually refers to a particular maze in Knossos on the Greek island of Crete, designed by Daedalus to contain the Minotaur: a ravenous bullhuman hybrid, which found human sacrifices particularly appetising. Theseus navigated these tortuous underground passageways by means of … Continue reading
Posted in Ciphers
Leave a comment
MODA: Inequalities
I imagine you’re all eagerly anticipating Cipher Tuesday, which is only a couple of days away now! Meanwhile, the sixth chapter of MODA, namely ‘Inequalities’, is available for download. Preface Combinatorics I (enumerative and geometrical combinatorics) Linear algebra Combinatorics II (graph theory) Polynomials Sequences Inequalities Projective geometry … Continue reading
Posted in MODA
Leave a comment
163
There is a reasonably popular card game entitled 24, where players attempt to derive 24 by applying basic arithmetic operations to a set of four positive integers. For example, the provided integers may be {3, 3, 8, 8}. A solution must … Continue reading
Posted in Uncategorized
Leave a comment
Antikythera mechanism
Near the beginning of the 20th century, a shipwreck was discovered. It contained a horde of treasure en route from Greece to Rome, including a lifesize bronze head of a philosopher. The most valuable treasure, however, was a 2000yearold analogue … Continue reading
Posted in Uncategorized
3 Comments
MODA: Sequences and Polynomials
It’s reached this time of week again, so I’ve uploaded the fourth and fifth chapters of Mathematical Olympiad Dark Arts. Enjoy! Preface Combinatorics I (enumerative and geometrical combinatorics) Linear algebra Combinatorics II (graph theory) Polynomials Sequences Inequalities Projective geometry Complex numbers Triangle … Continue reading
Posted in MODA
Leave a comment
Lizard and Spock dice
Continuing the theme of magic squares, we begin with the unique simplest nontrivial magic square. It contains the integers {1, 2, …, 9}, one in each square, such that the rows, columns and diagonals all sum to 15. Remarkably, the converse is … Continue reading
Posted in Uncategorized
Leave a comment
Linearbounded automata
If we provide a bogstandard computer with an infinite data store, it suddenly becomes a Turing machine: capable of answering any question answerable by any digital computer. Even quantum computers are no more powerful; they are merely faster. For example, a quantum … Continue reading
Posted in Uncategorized
Leave a comment
Lunisolar calendars
Here’s the post I promised you a while ago. I wrote the first part of this in an email on Burns’ Night of 2011, and the main idea (which Alex Bellos termed the ‘Goucherian calendar’) was mentioned in the Guardian. … Continue reading
Posted in Uncategorized
Leave a comment