Author Archives: apgoucher

(I’m testing out the functionality of the cp4space Facebook page. Hopefully, this post should be automatically published there.) In most familiar board games, cubic dice are used on the basis that each face is equally likely to face upwards. In … Continue reading →

In three dimensions, the familiar cross product is a bilinear function expressible in terms of the Levi-Civita alternating tensor. Specifically, a = b × c can be written as ai = εijk bj ck, which has the following beautiful properties: Bilinearity: … Continue reading →

Given a finite alphabet Σ of size s and an integer n, a de Bruijn sequence is a cyclic string of symbols, such that each n-symbol string over Σ appears exactly once. For example, taking Σ to be an alphabet of … Continue reading →

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 →

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 right-angled triangle with rational side lengths have an area of … Continue reading →

The competition known as the Mathematical Ashes was created by analogy with the better-known 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 →

The von Neumann universe V is the hierarchy of all set-theoretic 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 →