The fifth group of essays from the 2021 Teddy Rocks Maths Competition come from entrants with names beginning with the letters J, K or L. The showcase will take place throughout May with the winners being announced at the end of the month.

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 2022 so be sure to follow Tom (Instagram, Twitter, Facebook, YouTube) to make sure you don’t miss the announcement!

All essays can be read in full (as submitted) by clicking on the title below. If you enjoy any of them please let the author know by leaving a comment.

Jadesola discusses De Casteljau’s Algorithm and how it can be used to create more realistic animations.

Jiayi explains why the golden ratio is the ‘most irrational’ of all the irrational numbers.

Joe gives an example of how maths and politics intersect through Arrow’s Impossibility Theorem.

Joe provides a beginner’s guide to Neural Networks and how they are used in Machine Learning.

Joel investigates some of the statistics of the COVID-19 pandemic and asks us all to be vigilant when it comes to misinformation.

Johnny gives a brief overview of the history of pi and how it was calculated from ancient times to the modern era.

Jonny discusses the benefits of creative thinking in mathematics through the example of imaginary numbers.

Karrar explains how to construct the nth-term for almost any sequence and uses the method to uncover a ‘hidden sequence’.

Kevin dives into the history of cryptography, from Ancient Roman ciphers, to modern day encryption.

Kleone provides an ode to circles – the simple shape with far-reaching consequences.

Kristiyan explores division by zero and why it is often seen as the mathematical equivalent to a black hole.

Kush talks topology, string theory and 6 ‘invisible’ dimensions.

Laura explains some of her favourite maths tricks so you can try them for yourself at home.

Lola provides an update on our knowledge of the primes, explaining the progress made so far and what is still to come.

Lucas introduces Game Theory through a series of examples from football and the animal kingdom.

Luca explains where Euler’s number comes form and why it is his favourite.