Manchester MathsJam recap, March 2013

Having been absent for last month’s MathsJam, I was keen to have a great time this month so I prepared some nice Easter-based things (since this is the nearest MathsJam to Easter). I thought about egg-shapes, and how to construct them, and came up with a few fun things. The turnout was huge (at its peak, 21+ε: one attendee was expecting) and we spread out over three tables.

To start with, we drew ellipses using a piece of string and two pins – using the top of a cardboard box as a base, we attached the string to both pins and then putting a pen against the string would mean that the sum of the distances to each pin would be a constant. While this didn’t strictly work hugely well, we got some ellipse-ish shapes. We then thought about how to make an ovoid which isn’t symmetrical in both axes, like an egg, and we’d found an insanely thorough webpage which suggested that putting three pins in a long isoscles triangle would give an ovoid shape (see: A Gardener’s Construction). This didn’t quite work either, partly because we’d read the instructions wrong and partly because our string was slightly elastic resulting in things basically indistinguishable from an ellipse. But we’d all had fun, which is what really matters.

In order to get closer to a proper egg-shape, we then busted out the rulers and compasses, using a method I found using arcs to construct lovely egg shapes. We also had coloured pencils to colour them in, but everyone was distracted at this point by the arrival of 24 Cadbury’s Creme Eggs, brought by one of our regulars as a treat for everyone. This sparked off a hilarious conversation about Creme Eggs, inspired by the question: given the recommended daily maximum of 2500 calories, how many Creme Eggs could the average human consume in a lifetime?

We calculated an answer using estimates as around 380,000 Creme Eggs, which is roughly 187 times the average human bodyweight – however, we also decided that eating nothing but Creme Eggs daily from birth would probably mean you would neither live as long nor weigh an average amount. You would also probably feel sick all the time, not to mention the issues around Creme Eggs not being on sale all year round. Can you freeze them?

We also briefly considered this: If you count one Creme Egg as taking one hour off your life expectancy, and you ate them at 2500 calories-worth per day (about 14 Creme Eggs), would there come a point when you’d know the next Creme Egg you eat will kill you? It later transpired this isn’t hugely well-defined, since you’d need to know how long your life expectancy was to start with.

We finished our eggy maths chatter by discussing the ‘White/Yolk Theorem’, which it turns out isn’t called that but is in fact called the ‘Ham Sandwich Theorem‘. This also inspired brief discussion of the Pizza Theorem. What’s your favourite mathematical result named after a foodstuff?

Moving on from Easter-themed maths, we played games of SET and a new Gigamic game called Gobblet, which I found at a university Maths Arcade and bought in the closing-down sale of the IRL branch of an excellent board game shop in Greenwich. The game involves making a line of four in your own colour, but some pieces can be placed over the top of others and change their colour, and only big pieces can be placed over smaller pieces, making the game have quite an interesting strategy challenge.

One of our new attendees challenged us to determine the value of $\displaystyle\lim_{n \rightarrow \infty} n – \sqrt{n^2 + n}$. It’s not zero!

We looked at this probability puzzle, which was tweeted by @MathUpdate:

Having announced immediately what he thought the answer might be, Paul and others wrote a quick Python program and determined they were right. I then discovered that we had a copy of the book it’s taken from in the bottom of the MathsJam box. We also tried these domino puzzles, in which you have to fit all the dominoes into the grid using logic and a pen; and we looked at this matchstick puzzle from Leicester MathsJam, coming up with some slightly strained definitions of ‘moving’ and ‘equilateral’. I was quite impressed by the solution.

Other MathsJams went really well this month too, with Cardiff and Newcastle communicating via Crisp Tube Enigma, and new startup Winnipeg MathJam enjoyed being in the same timezone as Washington DC MathJam and had a nice chat via Twitter.