SPS Mathematics Blog

This week, Louis gave a fascinating talk to the Maths Society all about fractals; those strange, endlessly repeating patterns that you find in nature. Whether you’re zooming into a fern, a snowflake, or a Sierpiński triangle, the same shapes keep appearing. Louis explained that fractals were originally developed to help describe rough, irregular shapes in nature – things that traditional geometry couldn’t handle. He introduced us to the Hausdorff dimension, a tool used to measure the 'size' of irregular shapes. Unlike traditional dimensions, it exists on a continuous scale. If you apply the Hausdorff measure to a shape for all dimensions lower than its true Hausdorff dimension, the result becomes infinite, a sign of its complexity. He demonstrated this using the triangle fractal. We also looked at the box-counting dimension, a more practical method for measuring how a shape scales as you zoom in. This helped us apply ideas to the Sierpiński triangle and understand how a for...

This Friday at the weekly meeting of MathsSoc, the members participated in a Maths quiz. Different teams competed against each other, tackling questions from an inconspicuous Japanese textbook, as well as IMO preparation papers. Over twenty minutes, teams divided the questions and attempted to conquer. Some rushed straight into the algebra-heavy sections, confident that their speed would pay off, while others carefully picked apart the geometry problems, preferring precision over pace. The atmosphere quickly became one of focused intensity: pages filled with half-finished calculations, muttered debates over which substitution to try next, and the occasional groan when an apparently simple problem turned out to have a hidden twist. Although the competition was light-hearted, there was a real sense of excitement in the room. The questions were unlike those found in the average textbook: they required creativity as much as method, forcing participants to think beyond routine exam prac...

We kicked off the 2025-26 Hans Woyda season with our fourth annual friendly with SPGS. A quick parity check showed that the girls’ school were responsible for hosting this year, and as such all I had to worry about was ferrying the 12 members of the SPS squad across the river to deposit them safely in Alexandra Shamloll’s capable hands. Once again, she immediately showed me up by having the audacity to further improve the selection of team names. Teams Alpha to Zeta had been replaced by Team Conway, Euclid, Euler, Gödel, Nash and Ramanujan, all of which were chosen by the senior SPGS pupils ready for our arrival. As ever, we competed with mixed teams, with the 4 th and U8 th pupils from one school joining the 6 th and L8 th pupils of the other, and once all of the SPS boys had found their allocated mathematician we were ready to begin. All six teams fared well on the starter questions, but Gödel took an early lead after only making one mistake, while Euler and Euclid fell slightl...

We were very lucky at Maths society to have Dr Honnor talk about The p-adic Numbers. He has summarised the talk below: "The -adic numbers, first defined by Kurt Hensel in 1897 are a cornerstone of modern algebraic number theory. The  in question here will be a prime number and in the maths society talk we looked at a way of defining these fantastic numbers. We begin by considering the standard decimal expansions of the real numbers. It is worth noting that even at this early stage there is something a little remarkable happening. On the left hand side of our calculation we have   which is clearly finite where as on the right hand side we have a summation involving an infinite number of terms. It is the fact that   gets small very quickly, as   tends to infinity, that makes this infinite sum possible. A consequence of this is that we can write any real number in the following way: Here   is an integer greater than or equal to   and the coefficients ...