
Recent Posts
Subscribe to Complex Projective 4Space
Archives
 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: July 2013
Cipher 38: 60 percent wordsearch
Update: In my blithering ineptitude, I accidentally missed the bottom row off of the cipher. It has now been amended, and should be a 20 × 20 grid: The backdrop is a photograph of the Dumbbell Nebula, which I captured over a year ago by … Continue reading
Posted in Ciphers
Leave a comment
Further news
As usual, I’ll start this post by mentioning the current state of the bounded gaps between primes project. The current values are , with an unconfirmed result giving a value of H below 5000. It’s surprising how far these sieve methods … Continue reading
Posted in Uncategorized
Leave a comment
Converting problems into elliptic curves
Several geometric problems and Diophantine equations can be converted into the task of finding rational points on elliptic curves. The canonical example is to determine for which rational numbers n can a rightangled triangle with rational side lengths have an area of … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 37: Honeycomb II
As 37 is a centred hexagonal number, I decided to opt for a vaguely hexagonal arrangement: As usual, there is a passwordprotected solvers’ area.
Posted in Ciphers
Leave a comment
Mathematical Ashes
The competition known as the Mathematical Ashes was created by analogy with the betterknown cricketing Ashes, and is an annual competition between Britain and Australia. At the moment, Britain is in the lead, with Australia attempting to reduce the gap. … Continue reading
Posted in Uncategorized
Leave a comment
Von Neumann universe
The von Neumann universe V is the hierarchy of all settheoretic sets. It is itself too large to be a set, and therefore is considered to be a proper class. There’s a very simple systematic construction of the von Neumann universe, … Continue reading
Posted in Uncategorized
8 Comments
Cipher 36: Concube cum cerebro
Despite currently suffering from hay fever, I was able to combine the following attributes into a cipher: The title is in alliterative Latin. The index of the cipher (36) is a perfect square, as is the length of the cipher … Continue reading
Posted in Ciphers
Leave a comment
Generalised TFAE
The abbreviation TFAE (the following are equivalent) is often used in the statement of various theorems. Of course, a completely synonymous phrase would be ‘any one of these implies the other n − 1′. This then admits a natural generalisation … Continue reading
Posted in Uncategorized
Leave a comment
PSL(2,Z)
A particularly important function is Klein’s jfunction. It is defined on the upper halfplane of the complex numbers, and is incredibly symmetrical. For example, it is periodic, and thus invariant under translations by integers: It is also invariant under a larger … Continue reading
Posted in Uncategorized
Leave a comment
Cipher 35: Adjacency mania
You may find this one easier if you’ve attempted Cipher 6.
Posted in Ciphers
Leave a comment