Category Archives: Uncategorized

Let’s consider the group S6 of permutations of {1,2,3,4,5,6}. For fairly boring reasons, we can find S5 living inside there — the subgroup which fixes the element ‘6’. More generally, S(n-1) is contained within Sn. S6 is special, though, since … Continue reading →

Suppose we took a solid unit cube and balanced it on a vertex. Next, we spin the cube really quickly about the vertical axis, producing a solid of revolution: Clearly, the top and bottom are two identical cones produced by revolving a line segment passing … Continue reading →

As a brief summary, I posted about the three-dimensional generalisation of a particular two-dimensional problem by Alexander Betts. In case you haven’t read it, or didn’t understand it, I’ll explain the ideas again here. A finite set S of n points in d-dimensional … Continue reading →

If you take an object and rotate it by 360° about a particular axis, it will return to its original orientation. Certainly, every object you’re likely to have seen obeys this basic principal. If you’re naive, you may actually believe … Continue reading →

So, what’s up with that, right…? In case you haven’t heard of the field with one element, it’s a totally stupid non-existent thing that doesn’t exist. Nevertheless, its blatant non-existence did not deter several people from extensively investigating it, with … Continue reading →

Suppose we have a particularly ravenous cat (Felis sylvestris) chasing some particularly tasty mice (Mus musculus, if I remember correctly) across the vast expanse of the real Eculidean plane R². The most interesting case is when mice and cats move at … Continue reading →

A few weeks ago, arguably the greatest fan of cp4space invited me to his birthday party at the Eagle. As I mentioned in my speech, this was where Watson and Crick unveiled their proposed double-helix structure of DNA. Interestingly, the … Continue reading →

Hunter Spink gave me an interesting problem about a beach ball inscribed in a wire tetrahedron, since its most elegant solution uses techniques explored in the tenth chapter of Mathematical Olympiad Dark Arts. Rather than give you the problem now, … Continue reading →

Alexander Betts (nee Luke) posed an interesting problem in combinatorial geometry for the Romanian Masters of Mathematics 2011: We have a finite set S of n points in the plane, {A1, A2, …, An}, such that (for all i and j) the … Continue reading →

It’s Guy Fawkes Night now and I’ve had to update the seasonal banner yet again. There are a few late items of news I would like to mention: Firstly, thanks go to everyone who has sent me feedback regarding MODA; I have … Continue reading →