The sixth group of essays from the 2022 Teddy Rocks Maths Competition come from entrants with surnames beginning with the letters M-N. 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!

Maria Julia tells the story of John Conway – a mathematician that was able to bridge the gap between academics and the general population through the use of mathematical games and puzzles.

Nishant calculates the note we would hear if the infinite Gabriel’s Horn existed and could be played as an instrument.

Shuayb breaks down the mathematics underpinning modern cryptography, from modular arithmetic to Euler’s Totient Function.

Steven shows how any number in the base-10 decimal system can be broken down into an equation involving the sum of its digits.

Eva explores the properties of water through the lens of mathematics.

Shanjeev defines the golden ratio and identifies how it has been used throughout history to create beautiful buildings and pieces of art.

Aidan gives a detailed overview of the Kalman filter and how it can be used to help to remove statistical noise from data.

Parth analyses the equations used to determine the exit velocity required to leave Earth and the orbital velocity of the International Space Station.

Atul provides a brief history of the properties of prime numbers and the various areas of mathematics that have been used to try to understand them.

Simeon explores the Collatz Conjecture through a series of graphs that reveal the underlying structure of the problem.

Gayane explains two models that can be used to analyse sleep patterns and discusses the important insight they can offer.

Images: MathEnthusiast314 on Reddit and Roy John.

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“An integral part of music” was a really nice essay. In my humble opinion, I found some parts a bit hard because I am not an expert in the music field. As a suggestion, I feel like that a brief introduction to music theory would quite improve the quality of the entry. Altough, the work on the maths behind the harmonic series and the equations to assess the sound produced by the Gabriel’s Horn where really interesting. I learnt a lot from it.

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