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Our popular Maths Circle lectures have been well attended this year! Students, staff and guests have listened avidly to experts in the field. Akshay and Uthman, both in Year Twelve, share their experiences below.

Synths, the Universe and Doodling

Last week’s lecture, the second in the series, presented by Dr. Phil Ramsden of Imperial College London, proved particularly captivating. The focal point of his presentation aimed to unravel a compelling query: what connects sixteenth-century arguments about astronomy and cosmology, the structure of your inner ear, electronic music and a clockwork doodling machine?

Throughout the hour-long session, we embarked on a journey through the evolution of planetary models, from the geocentric model to Copernicus’ heliocentric frameworks. Dr. Ramsden adeptly illustrated how the motion of celestial bodies can be depicted through a series of epicycles- a phenomenon wherein smaller circles orbit around larger ones. Delving deeper, we explored the auditory realms, discerning the distinct sounds produced by various waveforms such as triangular and square waves.

Astonishingly, we discovered that these sounds could be deconstructed into elemental sine waves, which, when amalgamated through synthesis, produced the melodies we heard. Moreover, the revelation that our cochlea serves as nature’s synthesiser, detecting these sine waves, which are then put together in our brains to grant us the gift of hearing, was nothing short of awe-inspiring. Intriguingly, we drew parallels between celestial mechanics and childhood pastimes, unveiling how the sketch-a-graph toy employs epicycles to sketch diverse shapes.

Yet, what truly ignited my curiosity was the notion that planetary orbits, governed by epicycles, could be articulated through sine waves. This revelation made me ask myself: if each celestial body’s trajectory can be expressed through epicycles, which, in turn, can be represented by sine waves, does this imply that every cosmic entity emits a distinctive sound? Might these celestial bodies orchestrate the enigmatic melodies of space? My inquiry elicited a ripple of muffled laughter from the audience, swiftly followed by a resonant "Oooh'' from Dr. Ramsden—a reassuring echo that my curiosity had merit.

To my astonishment, Dr. Ramsden confessed that my query had never before crossed his path. My innocent question had, unexpectedly, kindled a flame of curiosity within him. Thus, what commenced as a quest to satisfy adolescent curiosity culminated in an unforeseen mission: to unveil the ethereal melodies of celestial bodies.

Thank you to Dr Ramsden for his speech and also to Mr Jerrom for co-ordinating the lecture series.

Uthman, Year 12

Differential Equations and How To Solve Them

Our third lecture saw the return of Dr Cooper, with an exciting lecture about differential equations, which helped us understand how Mathematics serves crucial real-life phenomena.

After captivating the audience with his vast experiences in Mathematics, Dr Cooper was quick to return to what we were all familiar with: GCSE Mathematics. The linear equations, simple differentiation and exponential functions caused the audience to sit smugly in their seats. However, this was only temporary!

As Dr Cooper moved up the gears into A-Level differential equations, the smug look quickly faded for some, as we jumped into the unfamiliar of separable differential equations. Despite this, with the help of concise explanations, elevating animations and pure enthusiasm, it wasn’t long before the unfamiliar became familiar.

All that Dr Cooper had addressed thus far were simply the foundations for the greater sensations at hand: the uses of differential equations. The most rousing applications involved Dr Cooper’s own work on Plasmid Stability in Microorganisms, as well as the renowned Simple Harmonic Motion accompanied by Maxwell’s Equations.

Whilst for most the Mathematics behind these was extremely challenging, we were left with an immense appreciation for the importance of Mathematics in the real world. With the audience inspired, we are all grateful for Dr Cooper’s return to the JJ Hall Stage.

Akshay (Year 12)

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