From aliens to bees via tattoos…

A short review of intern Joe Double’s work with Tom Rocks Maths over the summer of 2018. Written for the OUS East Kent branch who provided funding for the project. 

‘First of all, I must thank you again for the grant, and for the warmth and friendliness at your event; it was an absolute delight to give my presentation and talk to your members, as it has been interacting with you in general.

I had the opportunity to work with one of my tutors over the summer to produce pieces for a general audience about complex mathematical topics. Without the help of the OUS East Kent group, I couldn’t have taken up this opportunity – with their grant’s help, I was able to afford to live in Oxford through a large part of the summer, allowing me to work in close contact with my tutor and use his studio for creating the videos and audio pieces I worked on. The OUSEK grant can be put to use far more flexibly than those from bigger schemes (which always have preconditions to meet about how the project will apply to industry, say), so I couldn’t recommend applying more if you have an idea for a project for your time at Oxford which is on the unusual side!’

Pieces I produced during the project:

Why do Bees Build Hexagons? Honeycomb Conjecture explained by Thomas Hales

A video I edited of Tom (my tutor) interviewing Thomas Hales about the mathematics behind beehives.

Would Alien (Non-Euclidean) Geometry Break Our Brains?

My main video, written, filmed and edited by me, about demystifying non-Euclidean geometry.

Take me to your chalkboard

My main audio piece, where I interview Professor Adrian Moore (also of St Hugh’s) about what philosophy can tell us about how aliens might do maths.

Maths proves that maths isn’t boring

An article about Gödel’s incompleteness theorems, and how they show maths is always risky.

Getting tattooed for science…

An audio piece I edited about a tattoo Tom got of the Platonic solids.

Alien maths – we’re counting on it

An article about how we use the mathematics of prime numbers to send messages to the stars.

Play Nice!

An article about a game theory paper which could amongst other things help stop deforestation.

The original article was published on the OUS East Kent website here.

Getting tattooed for science…

Listen to me being tattooed whilst attempting to describe the process, and hear from my artist Nat on his experience as a tattooist…. all in the name of science.

You can also watch a short video below of the tattoo being done from the perspective of the artist.

Audio edited by Joe Double.

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…

Screen Shot 2017-05-02 at 22.37.47

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.

WordPress.com.

Up ↑