
Recent Posts
Archives
 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
Categories
Meta
Corresponding Facebook page:
Follow me on Twitter
My Tweets
Monthly Archives: November 2013
Brouwer’s fixedpoint theorem
Many theorems in analysis have combinatorial analogues, which turn out to be equivalent (in the sense that one can be derived from the other, and viceversa, using significantly less maths than is necessary to prove either from first principles). A particularly … Continue reading
Posted in Uncategorized
2 Comments
Crash course in Gaussian integers
Yesterday, I attended the UKMT mentoring conference in Murray Edwards College (affectionately abbreviated to ‘Medwards’), which mainly consisted of an excellent dinner in the Fellows’ dining room and informal discussion about various topics. Speaking of mentoring, I recently prepared for one of … Continue reading
Posted in Uncategorized
6 Comments
Bounded gaps update
A few months ago, Yitang Zhang announced that there are infinitely many pairs of primes, separated by a distance no more than 70000000. This initiated an extensive collaborative effort (known as polymath8) to reduce this bound by optimising different parts of the proof, until … Continue reading
Posted in Uncategorized
Leave a comment
Hearing the shape of a drum
(There appears to be a recent weeklong awkward silence on cp4space, partially due to the end of Season II of ciphers. Here’s an attempt to rectify it.) Suppose we have a square drum, consisting of a membrane fixed at its perimeter. The membrane … Continue reading
Posted in Uncategorized
5 Comments
Quantum logic gates
You are probably aware of classical logic gates, such as the Boolean AND and OR gates. The input(s) and output(s) of a logic gate take values in the set {0, 1}, usually identified with ‘false’ and ‘true’, respectively. One example … Continue reading
Posted in Uncategorized
5 Comments
Yf and only Yf?
There are plenty of triangle centres. One of the lesserknown triangle centres is Kimberling’s X(174), the Yff centre of congruence. It can be defined by considering lines known as isoscelisers, which are lines perpendicular to the angular bisectors of the triangle. If … Continue reading
Posted in Uncategorized
3 Comments
Gosper’s Pyrominia animation
As mentioned in a previous post, a pyritohedron is a (not necessarily regular) dodecahedron with pyritohedral symmetry. Up to scaling, any pyritohedron can be parametrised with the following coordinates: (±1, ±1, ±1); (±x, ±y, 0) and permutations thereof. For the … Continue reading
Posted in Uncategorized
2 Comments