SPS Mathematics Blog

At the end of last Friday 7 th   November, I met the second iteration of the SPS Hans Woyda team in the atrium as we prepared for the unusually short journey to our first away match of the season. Unfortunately this meant that there was barely any time for me to pester Haoming (4 th ), Ehan (6 th ), Andrew (L8 th ) and William (U8 th ) with warmup questions on the trip over, and before I had even managed to get through three sections’ worth we had arrived at Harrodian. After a brief walk through the site to the prepared classroom (during which I admitted, to my embarrassment, that after eight years at St Paul’s I had never stopped to wonder where the name of our neighbouring school comes from!) the team took their seats and the match got underway. Both teams had a strong start, getting three out of the first four questions correct, with a counting slip on our part made up for by a summation slip on theirs. The next four starter questions caused a few more problems on both sides, no...

On Tuesday 30 th  September, we welcomed Emanuel School for the first official match of the 2025-26  Hans   Woyda  competition. The SPS team of Aryan (4 th ), Rafael (6 th ), Zicheng (L8 th ) and Aman (U8 th ) were already warmed up from the friendly against SPGS, and they were further buoyed by the support of Adavya, William and Andrew who came to spectate (along with the inimitable Dr Stoyanov). The team assisted me in arranging the classroom into my famous Battle Chevron formation (patent pending) before taking their seats to await their opponents. Once the Emanuel team had arrived and settled into their places we had a momentary pause while one of the tables was adjusted to avoid a stream of sunlight going directly into their Year 12’s eyes (which I insisted was not a deliberate act of sabotage!), after which I projected the slides, hushed the audience and handed out the first set of questions.   SPS hit the ground running with a perfect set of answers to th...

House Mathematics started this week and it already looks like a fiercely fought contest. With house points on the line, who can blame them! It is true that Paulines love competition but House Mathematics is certainly one of the highlights of the year. The competition is formed of three rounds, the first round, semi finals and finals. In these, a student from each year group partakes in quickfire questions, similar to those of the Hans Woyda, in a head to head battle with another house. All 8 houses played in the first round:  Langley 32 Stewart 26 Cloete 34 Nilsson 26 Gilks 24 Harrison 22 Blurton 34 Warner 26 These were hosted in individual classrooms. I personal thought what was most impressive, was the crowd of supporters who came to cheer on their houses. In some rooms it was hard to find a place to sit. Well done to all who were involved and a special thanks to the 8 Maths teachers who gave up their time to run the first round of the competition. The Semi Finals are up ne...

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...