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The perfect formula for mathsiness

It’s mid-January, which means it’s time for the tabloids to trot out their annual “this is the most miserable day of the whole year!” story — before they spend the rest of the year blaming immigration, youth and political correctness for problems they’ve spent the last year stoking up.

Ahem.

AS maths results and batting averages

Phil Harvey gave a talk on this subject at last November’s MathsJam conference. We liked it so much, we asked him if we could put it on the site. Phil’s kindly written his talk up as an essay for us.

I am 64¼ years old and I’ve been a maths teacher all my working life. In that time things have changed. Long gone are the days when gowned masters would sweep in, silence any murmur with half a raised eyebrow, and delight compliant uniformed schoolchildren with chalk-covered boards of mathematical exposition.

No, you’re right. That never happened outside the covers of Goodbye Mr Chips, even in my day.

The reality then. Schoolchildren have morphed into learners. Exam results rule. Quality (in the sense that Orwell might have used the word) is managed by quality managers. And so our working lives are driven by the pursuit of Ofsted targets, success rates, achievement rates, benchmarks, observation grades, results. And every joyless lesson has its own lesson plan, with aims, objectives, learning outcomes and action points. But above all, those damned results – and every year, year after year, they had to IMPROVE.

Well I was no good at any of this stuff – and consequently I always got on very badly with my managers. Until one year…

Deck the halls with τ of holly, formula-la-laaa!

Christmas is a time for giving, celebrating, family and magic. But did you know it’s also a time for equations? Department store Debenhams has decided to honour this recent Christmas tradition by tasking at least two members of Sheffield University’s undergraduate maths society to come up with formulae for ‘a perfectly decorated Christmas tree‘, picked up by The Sun, The Metro and others.

Christmas Tree

Photo by Aleksandar Cocek, used under a Creative Commons licence.

Previous festive howlers include ‘the formula for the perfect family Christmas‘ (sponsored by The Children’s Society to promote a book) and a prior stab at ‘the equation for the ideal Christmas tree‘ (sponsored by B&Q), which are just nonsensical strings of abbreviations. However, unlike those examples of naff-ematics, the Sheffield tree-decorating equations make enough sense for me to take a critical, overly-serious look at them on their own merits, and show how you might begin to come up with something more rational.

Radii of polyhedra

(At last month’s big MathsJam conference, we asked a few people who gave particularly interesting talks if they’d like to write something for the site. A surprising number said yes. First to arrive in the submissions pile was this piece by Tom Button.)

The formula for the surface area of a sphere, $A=4\pi r^{2}$, is the derivative of the formula for the volume of a sphere: $V=\frac{4}{3}\pi r^{3}$.

This result does not hold for a cube with side length $a$ if the surface area and volume are written in terms of $a$. However, if the surface area and volume are written in terms of half the side length, $r=\frac{a}{2}$, you get the surface area $A=24 r^{2}$, which is the derivative of the volume, $V=8 r^{3}$.

What I did on my holidays, by Colin (aged 35 and a bit)

We’re all back from the big MathsJam weekend. We’ve got loads of material which we’ll start putting up once we’ve recovered our energies. Meanwhile, Colin Beveridge has sent in his report of the event.

Last weekend – as I’m sure all Aperiodical readers know – was the MathsJam annual gathering in Cheshire.

Now, I’ve always hated conferences. Loathed the bloody things. I resented travelling to them, resented preparing talks, resented the uncomfortable beds, the politics, the enforced niceness. I resented the nod-along-and-pretend-you-understand, the gabble-away-with-your-head-down-so-you-can-say-you-gave-a-talk, the questions-for-the-sake-of-advancing-pet-theories, the sessions that lasted weeks. I resented the trying-to-find-veggie-food-in-New-Orleans, the being-expected-to-show-up-for-everything, the having-to-keep-receipts, all of it.

I could have just stayed at my desk and played Tetris. But MathsJam is different.

Robert Schneider, Mathematical Musician/Musical Mathematician

(This article is based on an interview that was originally conducted for the podcast Relatively Prime)

Robert Schneider is a rock star mathematician. I do not mean that in the metaphorical sense, as when it is applied, with a rather unmathematical lack of precision, to celebrity mathematicians such as Terry Tao, Cedric Villani, or Timothy Gowers. I mean it in the most literal sense: Robert Schneider is a mathematician and Robert Schneider is a rock star.