Monthly Archives: November 2012

In 2001, Lee Sallows generalised the concept of a magic square, replacing the integers in each cell with subsets of the plane. He calls such a configuration a ‘geomagic square’ if the subsets in every row, column and diagonal can … Continue reading →

Tsukamoto and Miyazaki of Kyoto University have discovered that three states are sufficient to enable gliders to exist on a Penrose tiling, rather than four. The following video demonstrates their discovery together with a periodic emitter in an augmented rule: [youtube=http://www.youtube.com/watch?v=6xVLpP25DRQ] On … Continue reading →

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 →