The fourth group of essays from the 2022 Teddy Rocks Maths Competition come from entrants with surnames beginning with the letters I-J. The showcase will take place throughout May and June with the winners being announced at the end.

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 2023 so be sure to follow Tom (Instagram, Twitter, Facebook, YouTube) to make sure you don’t miss the announcement!

Lee documents all of the regular polyhedra from the standard shapes we learn about at school, to star polygons and duals.

Aidhid shows how mathematical concepts such as geometric series and calculus are used in Economics to build models that can aid decision making.

Radhika explains how simple error-correcting codes allow us to retrieve the original meaning from a corrupted message, and how these codes can be represented visually through sphere packing.

Sienna explores elliptic curves beginning with a definition of the equations and the operations that can be carried out on them, before explaining how they are used in modern cryptography, and their relevance to the million-dollar Birch-Swinnerton Dyer Conjecture.

Esa teaches the basics of fluid dynamics from Bernoulli’s Equation to Navier-Stokes, using the soft drink Fanta as an example.

Joshua introduces Einstein’s Field Equations and derives the Metric Tensor from first principles (including an explanation of the notation).

Henry summarises over 300 years of Knot Theory from Invariants to Polynomials via Reidemeister Moves.

Aleksandra identifies several occurrences of maths in the natural world, from the use of echolocation by bats, to sampling methods for a frog population.

Ugas explains why the leading digit in a random sample of numbers is more likely to be 1 than any other – a result known as Benford’s Law.

Arushee presents some infamous probability problems including Buffon’s Needle experiment which can be used to calculate the value of Pi, as well as the Total Expectation Theorem which is used to calculate the average log length following two cuts form a lumberjack.

Jash dissects Euler’s proof of the Basel Problem and shows how it can be used to calculate the infinite sum of any series of the form 1/n^(2k).