Maths, but not as you know it… (St Edmund Hall Oxford Magazine)

Dr Tom Crawford joined the Hall in October 2018 as a Stipendiary Lecturer in Mathematics, but he is far from your usual mathematician…

Tom’s research investigates where river water goes when it enters the ocean. A simple question, you might first think, but the complexity of the interaction between the lighter freshwater and the heavier saltwater, mixed together by the tides and wind, and pushed ‘right’ along the coast due to the Earth’s rotation, is anything but. The motivation for understanding this process comes from recent attempts to clean-up our oceans. Rivers are the main source of pollution in the ocean, and therefore by understanding where freshwater ends up in the ocean, we can identify the area’s most susceptible to pollution and mitigate for its effects accordingly.

To better understand this process, Tom conducts experiments in the lab and has conducted fieldwork expeditions to places as far-flung as Antarctica. What the southern-most continent lacks in rivers, it makes up for in meltwater from its plethora of ice sheets. The ultimate process is the same – lighter freshwater being discharged into a heavier saltwater ocean – and as the most remote location on Earth the influence of humans is at its least.

If you thought that a mathematician performing experiments and taking part in fieldwork expeditions was unusual, then you haven’t seen anything yet. Tom is also very active in outreach and public engagement as the author of the award-winning website tomrocksmaths.com which looks to entertain, excite and educate about all thing’s maths. The key approach to Tom’s work is to make entertaining content that people want to engage with, without necessarily having an active interest in maths. Questions such as ‘how many ping-pong balls would it take to raise the Titanic from the ocean floor?’ and ‘what is the blast radius of an atomic bomb?’ peak your attention and curiosity meaning you have no choice but to click to find out the answer!

Tom is also the creator of the ‘Funbers’ series which was broadcast on BBC Radio throughout 2018 telling you the ‘fun facts you didn’t realise you’ve secretly always wanted to know’ about a different number every week. From the beauty of the ‘Golden Ratio’ to the world’s unluckiest number (is it really 13?) via the murderous tale of ‘Pythagoras’ Constant’, Funbers is a source of endless entertainment for all ages and mathematical abilities alike.

And now for the big finale. If you are familiar with Tom’s work, you may know where we are heading with this, but if not, strap yourself in for the big reveal. Dr Tom Crawford is the man behind the ‘Naked Mathematician’ (yes you did read that correctly). To try to show that maths isn’t as serious as many people believe, to try to engage a new audience with the subject, and just to have fun, Tom regularly gives maths talks in his underwear! His ‘Equations Stripped’ series on YouTube has reached 250,000 views – that’s a quarter of a million people that have engaged with maths that may otherwise have never done so. His recent tour of UK universities saw several thousand students come to a maths lecture of their own accord to learn about fluid dynamics. It may not be to everyone’s tastes, but our current methods of trying to engage people with maths are failing, so why not try something new? This is maths, but not as you know it.

You can find all of Tom’s work on his award-winning website and you can follow him on FacebookTwitterYouTube and Instagram @tomrocksmaths for the latest updates.

The original article published in the Aularian magazine can be found here.

Tom Rocks Maths Episode 04

The fourth and final episode of Tom Rocks Maths this term on Oxide – Oxford University’s student radio station. Featuring my favourite shapes, cannibals with a hat fetish, the golden ratio and the weekly maths puzzle for you to solve. Plus, music from Foo Fighters, Green Day and Sum 41…

Funbers Golden Ratio

Next up in the Funbers series is the Golden Ratio… credited with explaining beautiful architecture, beautiful art and beautiful people. It appears everywhere in nature and may just hold the secret to everlasting beauty…

You can find all of the episodes in the Funbers series with BBC Radio Cambridgeshire and BBC Radio Oxford here.

Funbers 1.618…, 2 and e

The fun facts about numbers that you didn’t realise you’ve always wanted to know…

1.618… – THE GOLDEN RATIO

Why are some things nice to look at and others simply aren’t? Notre Dame Cathedral, the Great Pyramids, the Parthenon, Leonardo Da Vinci’s Last Supper… All great to look at and all created with the Golden Ratio. It’s a number, like any other, but the way it’s formed is what makes it so special. You take a straight line and then divide it up with the following rule: the short part and long part must be in the same ratio as the long part and the whole line. It sounds more complicated than it is. Let’s have a go…

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If we chop the line at the dot we divide it into two parts and we have three different lengths of line. The original line has length A, the short part B and the long part C. To get the golden ratio we must have B/C = C/A. Solving this with a little bit of maths (put A = 1 as it’s the original line and then you have two simultaneous equations with B + C = 1) tells us that we have to put the dot 0.618… along the original line – so just under two thirds of the way along. Now the clever part is that if you add the length of the long part 0.618… to the original length 1, you get 1.618… aka the Golden Ratio. It pops up everywhere in nature from sunflower petals to the spiral of a shell. It is even credited with the correct facial proportions that make people attractive.

2 – TWO

Double double toil and trouble… even Shakespeare loved the number two and he knows a thing (or two) about language. Two is a powerful number: it can mean two opposites or two partners. Friends and enemies, light and dark, good and evil – we like pairs. It’s also a really important number in maths. It’s the first even number, and we actually define even numbers as the ones that can be divided by two. It’s also the first prime number and the only one that is even. Remember, a prime number is one that has only two factors: itself and 1 – nothing else multiplies together to make it. So for 2, we have 1 x 2 = 2 and that’s it. For any other even number, say 4, we can divide it by 2, so 2 x 2 = 4. This means that 4 has three factors: 1, 4 and 2. So it’s not prime.

2.7182… – e

Euler’s number and also my favourite number – like the Navier-Stokes equations, when you have a tattoo of something it kind of has to be your favourite. It pops up anytime you start doing calculations with growth and growth rates. For example, let’s talk money. Suppose you have £1 and I give you two options for investment: I’ll either give you 1/12th interest every month for 1 year or I’ll give you 1/365th interest every day for 1 year. Which do you take?

It’s kind of a trick question because we can of course do the maths and see which is best… £1 after one month is worth £1 x (1 + 1/12) = £1.08. After two months we have £1.08 x (1 + 1/12) = £1.17, after three months we’re at £1.17 x (1 + 1/12) = £1.27 and so on. After one year our grand total is £2.61, not bad! Now what about the second option, well after one day we have £1 + 1/365 = £1 (plus a tiny bit). After one month (30 days) we have £1.09, so actually one penny more than option one. And after a whole year we have £2.71, so an extra 10p! So the pattern seems to be that the more often we are paid interest (despite it being a lower percent), the more money we get. What about if we are paid every hour? Well that’s 24 x 365 = 8760 hours in a year, at a rate of interest of 1/8760th per hour. The grand total for the year gives us £2.71, the same as before. Huh? Why didn’t it increase? The answer is it actually did, but you can’t have part of a penny.

What’s actually going on here is that we are calculating the number e to higher and higher levels of accuracy. We’ve been working out the answer to (1 + 1/n)n for n = 12, 365 and 8760. If we let n go to infinity then we get the exact value of e. Amazing, right? Probably so amazing you just want to get the first 100 digits of the number tattooed in a spiral around your arm…

You can find all of the funbers articles here and all of the episodes from the series with BBC Radio Cambridgeshire and BBC Radio Oxford here.

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