Maths Society Student Speaker

Maths Society Student Speaker - Louis: Fractals

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 formula like rd=nr^d = nrd=n relates to self-similar structures.

The 16+ Mathematics Entry Exam for St Paul’s School

The mathematics entrance exam at 16+ is taken in November for entry to study A Levels in the following September. The content of the exam is the Edexcel IGCSE syllabus but does not include the topics of arithmetic series and differentiation. The emphasis is on number and algebra skills. The test for entry in September 2026 onwards will be non-calculator. When you apply to St Paul’s, we need to know whether you intend to take single mathematics A Level or further mathematics A Level. Pupils who do well on the entrance papers across all their chosen subjects are invited for interview. Interviews are taken by subject specialists at St Paul’s School and last 20-30 mins. The aims of the interview are to: gauge your ability to apply the GCSE mathematics skills in unfamiliar questions. to understand your reasons for choosing the subject. to investigate the additional problem-solving skills you have developed through classes and your independent studies. We realise that not ...

Hans Woyda Final vs King's College School Wimbledon

Yesterday, six months after kicking off the 2024-25 Hans Woyda season with our annual friendly against SPGS, we were at long last on our way to the final. There was a palpable tension around the school site and an unmistakable atmosphere of excitement and anticipation, making it abundantly clear that the entire school had their minds on that afternoon’s Mathematics fixture. As I set off for the match with Yidong (4 th ), Shyamak (6 th ), Adavya (L8 th ), and Eason (U8 th ), accompanied by Dr Stoyanov for moral support and intimidation, pupils and staff had even gathered by the towpath to wish them well; unfortunately, they all seemed to be facing the wrong direction, but it was touching nevertheless. We made our way to the City of London School (which offered its services as neutral territory for the final), discussing tactics on the tube and working through a set of warm-up questions. We met the King’s College School Wimbledon side in the lobby as we arrived, and based on previou...

Problem Solving with Mykhailo

The maths society had the pleasure of welcoming one of our own, Mykhailo who presented a captivating talk on problem solving in mathematics. He began by telling us of his journey through mathematics, starting in Ukraine at the humble age of 7, where he agreed to compete in his first Olympiad in return for some Lego - a worthy reward. By the age of 11, however, he began to lose interest until a remarkable geometry teacher reignited his passion. From that point on, he was completely hooked on geometry, so much so that his Olympiad scores r eflected his singular focus: 0/7, 0/7, 0/7, and finally, 7/7, as he excelled in geometry alone. He, therefore, decided that it would be best for his progress if he stopped doing geometry altogether, focusing instead on the other 3 areas of math: Algebra, Arithmetic, and Number theory. He led us through a series of questions, seemingly impossible at the face of it but very manageable after explanation. Among the problems were a complex simultaneou...

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