Enjoy the fifth group of essays from the 2024 TRM Essay Competition, now proudly held in partnership with the Oxford University Department for Continuing Education. The showcase will take place throughout June and July with the winners being announced in August.

If you enjoy reading any of the essays, be sure to leave a comment to let the author know!

This essay uncovers the patterns in groups of shapes, and more generally across polygons.

This essay calculates the probability of a random collection of words appearing on a typewriter, based on the infamous phrase “a monkey on a typewriter would eventually write Shakespeare”.

This essay provides an overview of the technique of Fourier Analysis by calculating a mathematical expression for the step function.

This essay uses some simple formulae to estimate which dinosaur would have been the fastest.

This essay derives the Price Equation, which is used to model survival of a trait trough the process of evolution.

This essay explains how to create your own version of one of the most beautiful of fractals, the Mandelbrot Set, using a simple piece of Python code.

This essay hypothesises why fractals are so alluring to the human eye.

This essay exemplifies the importance of presenting mathematics in a manner that can be easily understood by your intended audience.

This essay investigates the range of medical applications of knot theory and how it has led to life-saving procedures involving RNA and DNA.

This essay presents several beautiful visualisations of chaotic systems including the butterfly-shaped Lorenz attractor.

This essay looks at various applications of trigonometry and Pythagoras’ Theorem.

This essay applies the tools and techniques of recurrence relations to analyse the structure of Sanskrit poetry.

This essay investigates the patterns formed by birds flying in sequence.

This essay explores a range of fractal patterns and computes formulae for their perimeter and area.

This essay showcases how a relatively simple sounding problem can lead to a convoluted, and complex, solution.