Category Archives: Uncategorized

This is the 100th article on cp4space, and is inspired by a discussion last night with Gabriel Gendler. Triangle centres with complex numbers Suppose we have a triangle in the Euclidean plane . We can identify the Euclidean plane with the … Continue reading →

I’m going to start by describing a game that seems completely unrelated to sphere packing. The Conway-Hamming game involves a half-infinite row of green apples, each of which can either point up or down: In any configuration, all but finitely … Continue reading →

Tim Large suggested to me a new idea of how to render meromorphic functions on the complex plane. Basically, we draw the surface of the Earth on the Riemann sphere (the codomain of the function), and colour each point on the complex plane … Continue reading →

The most popular music video of last year is, arguably, Gangnam Style by the famous Korean artist, Ψ. One of the noteworthy features is the presence of ‘accumulation points’ in the music; these occur at 1:07 and 2:29 in the … Continue reading →

Firstly, I’ll take this opportunity to wish James Cranch a marvellous 30th birthday. This post was inspired by the conception of a new ‘origami society’ at Trinity. Having never tried it before, it took me a while to decipher the instructions … Continue reading →

The Cayley-Bacharach theorem in projective geometry states that if two cubics share nine points (in sufficiently general position) and a third cubic passes through eight of those points, then it also passes through the ninth. Here, ‘sufficiently general position’ means … Continue reading →

Suppose we have a set of n people, and we want to encapsulate a particular relation which holds between them. For instance, the people who have featured on the cipher solvers page can be represented by a directed acyclic graph. … Continue reading →

This post contains miscellaneous topics which don’t deserve individual articles, but are still worth mentioning nonetheless. Stereographic map projections When you look at a map of the world, the most common projection is the Mercator projection. This is a conformal … Continue reading →

The Encyclopedia of Triangle Centres contains a collection of over 5000 different points in the plane of a triangle, represented by the letter X followed by an identifier. The well-known triangle centres include the circumcentre (X3), centroid (X2), orthocentre (X4) and incentre … Continue reading →