Enjoy the second 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 investigates what would happen if we allowed dividing by zero to be well-defined.

This essay discusses the use of L-systems to generate mathematical art through the use of simple repeating instructions.

This essay defines the golden ratio and looks at its occurrences in nature, including the gravitational force between two spheres.

This essay explains Kepler’s conjecture relating to the optimal way to pack spheres into a finite 3D space.

This essay applies the tools of mathematics to various aspects of the game of football, including player transfers, formation choice, and projectile motion.

This essay provides a detailed overview of a vast range of mathematical topics, as well as introducing a new variable to define division by zero.

This essay explains the importance of linear algebra in the techniques used for current machine learning algorithms.

This essay looks at how Leonardo Da Vinci incorporated the golden ratio, golden rectangle and the golden spiral into his most famous artwork.

This short essay discusses polynomials on a circle and how they are related to Euclidean geometry.

This essay explores the projections used to map the surface of the Earth onto the 2D plane, and why none of them will ever be completely accurate.

This essay analyses the relationship between the size of standard serving of different foodstuffs and their nutritional value.

This essay outlines a wide range of seemingly paradoxical statements about infinity, and how we can use them to determine the different sizes of the infinite.

This essay discusses the Fibonacci sequence and its relationship to the golden ratio and nature.

This essay looks at the mathematics of fractals, and how they can be applied to other areas such as coastlines and cancer research.

This essay takes an entertaining look at the intricacies of relativity, reference frames and the universal constant that is the speed of light.