The eighth – and penultimate – group of essays from the 2021 Teddy Rocks Maths Competition come from entrants with names beginning with the letters S or T. 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.

Saadhyan looks for occurrences of the golden ratio in two and three dimensional shapes.

Samuel takes us on a tour of some famous proofs demonstrating the different techniques available to mathematicians.

Seoyeon calculates how long it would take for the surface of the Earth to be covered in 3cm of plastic.

Shiloh defines a ratio of numbers.

Shivanshi explores space-time and the implications of an infinite universe.

Shuxin describes how to draw accurate sketches of linear, quadratic and cubic functions.

Sofiah investigates why the triangle is such a common shape across the world.

Soufiane derives the Euler-Lagrange equations and uses them to sole three famous problems.

Stefano motivates the need for complex numbers by solving quadratic equations.

Stephanie develops the standard SIR model to create a more realistic model for disease spread.

Taha tells the story of the proof of Fermat’s Last Theorem – over 350 years after the problem was set.

Ted introduces the concept of a Turing Machine and explains how it led to the development of the field of Computer Science.

Tierney presents several examples of humans inability to comprehend large numbers.

Tobi provides a beginners guide to entropy and how it links to the Second Law of Thermodynamics.

Tom explains the Divergence Theorem – one of the most important tools of both mathematicians and physicists.

Tye shows us how to turn any parabola into any other using only a translation and rescaling.

Thomas presents some of his favourite examples of mathematical modelling from the Navier-Stokes Equations, to the SIR disease model.