The fifth group of essays from the 2022 Teddy Rocks Maths Competition come from entrants with surnames beginning with the letters K-L. The showcase will take place throughout May and June with the winners being announced at the end.

The competition was organised with St Edmund Hall at the University of Oxford and offers a cash prize plus publication on the university website. It will be running again in early 2023 so be sure to follow Tom (Instagram, Twitter, Facebook, YouTube) to make sure you don’t miss the announcement!

Mustafa contemplates what we truly mean by ‘infinity’, and whether we should consider a ‘potential infinite’ and ‘actual infinite’ as two different entities.

Ingrid introduces the lesser-spotted Mill’s constant and demonstrates how it can be used to generate some very large prime numbers.

Bruno poses three problems – involving sleeping beauty, interrogation, and doomsday – and calculates some seemingly paradoxical probabilities.

Laksmana gives a detailed overview of the Ancient Greek mathematician Pythagoras and his work beyond the theorem which bears his name.

Joao provides a brief snapshot of the history of pi – from Archimedes and polygon approximations to Newton and the binomial theorem.

Vedant explores group theory from its roots in the symmetries of polygons, to the ‘periodic table of simple finite groups’ (including the infamous Monster).

Ryan shows how complex numbers can be represented as 2×2 matrices and demonstrates some of their properties.

Joel tells the story of their exploration of Sudoku, which culminated in a new-found appreciation of the mathematics that underpins modern computers.

Jihu gives us an insightful peek into the root of ancient Chinese mathematics and the work of Liú Huī.

Farhan helps to peel back the many properties and uses of the harmonic series, including a breakdown of the ‘desert problem’.

Helia presents a robust overview of complete quadrilaterals, culminating with their link to projective geometry via Brocard’s Theorem.

Looking to share a secret? Andrej shares a way to communicate efficiently in secret using elliptic curves.

Liu gives a fascinating overview of how the RSA cryptography system came to be (the story might surprise you!).