The seventh group of essays from the 2021 Teddy Rocks Maths Competition come from entrants with names beginning with the letters O, P or R. 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.

Oscar starts with the infamous Fibonacci sequence and extends it to the ‘Tribonacci’ and ‘Infinity-bonacci’ sequences.

Paige takes us sailing into the world of nautical mathematics – from bearings to stability calculations.

Paolo journeys into the worlds of graph theory and topology via the famous bridges of Koenigsberg.

Payal explains how it is theoretically possible for two twins to exist and yet be different ages.

Peter solves his favourite type of equation with some assistance from famous historical faces.

Philip investigates the problem of projecting a sphere onto a plane through the lens of world maps.

Pierce explores elliptical curves and how they are used to send information securely online.

Poppy discusses some real-world applications of statistics in the form of ‘sampling’.

Rabiah imagines a hypothetical world where we no longer use the decimal – or base 10 – system.

Rachael explains the friendship paradox and why your friends will always have more friends than you do.

Rehman models the interaction between animal populations in a predator-prey system.

Rhea takes a detailed look at the most famous equation in maths, explaining just why it is so beautiful to so many.

Ria’s search for a relationship between music and maths takes her back to Ancient Greece and the work of Pythagoras.

Rick dives into the world of roulettes with a showcase of cycloids, epicycloids and the brachistochrone problem.

Rita provides a detailed overview of the links between mathematics, art and music with an analysis of famous artists and musicians – both past and present.

Robert explains an intuitive derivation of the binomial distribution from some simple examples.

Ross investigates the history and origins of the most common mathematical constant.

Ruby-Jean praises all things zero – the number we simply cannot live without.

Ruth analyses the portrayal of mathematicians in movies and asks whether the representations are fair and accurate.