Eltham College Scholarship Programme

In today’s session with Year 9 Athenaeum, Mr Broncz looked at cyclic patterns in recurring decimals. Building up from simple ideas about the relationships between fractions and decimals via the Mathematician’s old friend the Prime numbers, the students began to see how what appeared to be a rather random links were in fact part of a beautiful cyclic pattern. Not only do these patterns allow the impressively swift response to questions about fractions as decimals, but more significantly, show how a different branch of Maths can illuminate the challenges of another, as most famously seen in Andrew Wiles’ solution to Fermat’s last theorem, involving modularity theorem.

Mr Broncz left the students an interesting problem to ponder, is there a predictable pattern to the patterns?

The lesson forms part of the Scholars Programme which includes workshops and lectures overseen by our Head of Academic Scholarship, Mr Cavendish.