Author Archives: apgoucher

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 →

There are plenty of triangle centres. One of the lesser-known 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 →

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 →

The 50-pence and 20-pence coins are regular curvilinear heptagons, where each edge is a circular arc centred on the opposite vertex. One may ask why the coins have such an unusual shape. One possible answer is that it is impossible … Continue reading →

It is a well-known fact, attributed to Cantor, that the set of rationals is countably infinite or, equivalently, we can find a bijection between the rationals and integers. These are easy to construct, but typically quite ugly. If you want … Continue reading →

Breaking news: A £500 prize for the most elegant solution in the British Mathematical Olympiad has been founded in the memory of Christopher Bradley, whose contributions to the United Kingdom Mathematics Trust were both plentiful and invaluable. Amongst his portfolio is the bestselling … Continue reading →

Here are some primarily mathematical double-entendres conceived by members of the Trinity Mathematicians’ Alcoholic Society. Some of them are biological or particle-physical, but never mind. Also, some names are censored for legal reasons. Disclaimer: I accept no responsibility for any offence caused … Continue reading →

You have probably encountered the 15-puzzle, where all but one of the squares of a 4 × 4 grid are occupied by counters. The only acceptable moves are to move a counter into an adjacent unoccupied square. Sam Loyd challenged … Continue reading →