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Maths Jam Conference 2013 Session 2

November 11, 2013

Continuing the maths talks…

Christian Perfect

Christian talked to us about the enneahedron. Christian has found a net for which this 3D shape with nine sides which is a non-Hamiltonian polyhedron in which every face has the same number of edges. It also has D6 symmetry.

An interesting talk with a pretty shape to look at (Christian had one made) but to be honest, he does a better job of explaining it over at the aperiodical.com (link to article) (link to net)

Alistair Bird

Alistair was discussing possibilities for gambling when both people want to bet on the same team winning. Before going into detail on that, he set up an interesting example where Albert has an item he values at £8. Bernard values the item at £12 and Albert sells it to Bernard for £10. In this case, both are happy and feel they’ve got a good deal. I’m sure this is a simple case of economics but it interested me.

He went on to discuss the possible ways of betting on the outcome of a football match when both think the same team will win but with different degrees of certainty. I’ll be honest and say I got a bit lost but I suspect this was due to the 5 minute limit and the threat of being Rick-rolled.*

Michael Gibson

Michael was interested in biased coins. Imagine you have a very large bag of coins in which there is a uniform distribution of biases. There’s a coin that is always heads, one that’s perfectly fair, one that’s always tails and every variation in between. You’ve pulled one out, flipped and got a Head. What’s the chance that it’ll be head next flip?

Another interesting idea (I won’t spoil the thinking behind the solution) but it does mean that Micheal is considering buying 840 blank dice to simulate the puzzle….

John Foley

John started by telling us that if a school removes one primary lesson of maths a week and replaces it with chess, this improves their maths ability.

John has created a new type of chess/maths puzzle in which there’s a piece in each corner and you consider how many pieces are attacking each corner. I really liked the puzzles and you can find the presentation here. I’ve passed them onto the two people that run my school’s maths club and John is interested in hearing feedback. His twitter handle is @chessscholar

Ken McKelvie

Ken is from the university of Liverpool’s maths outreach team. He was relaying the importance of communication skills in maths education and said (acknowledging that he was generalising) that at 16-19, the teachers feel that there is no time and it’s not examined anyway. At university, it’s not seen as real maths.

I agree with Ken a lot and hope there is room for communication skills becoming common place in universities.

Ewan Leeming

In a surprising change of pace, Ewan took us through some interesting puzzle aspects of navigational rallying. He likened it to ‘doing sudoku on a roller coaster’.
I didn’t get a chance to play with it much (I think people did in the evening after I’d gone) but it looked worth pursuing. There are obvious links to geography and use of coordinates too.

Yuen Ng

Yuen is currently studying A level maths and was the youngest presenter. Along with his tutor, he’s been looking at the forms of graphs, and where these appear in ‘real life’.
After looking at a couple of cardioid graphs

 \left(x^2+y^2-2ax\right)^2 = 4a^2\left(x^2 + y^2\right).\,

and showing us their pictures in soup and with carefully placed light sources and mugs, he moved on to a graph he’d co-invented and named the haemorrhoid. [note: a link to an image/equation would be fantastic please]
A confident presentation and I suspect we’ll be hearing more from Yuen in the future.

Liz Hind

This was the third in a trilogy of Liz’s presentations about the Egyptians. The first two were at previous maths jams so I haven’t seen them but that didn’t matter.
Liz showed us that Egyptians must have used maths when considering their town planning maps. They also set out their fields in highly geometrical patterns to allow the collection of taxes fairly and efficiently.
There was also an image of a tablet and evidence that this was the first known example of a spreadsheet.
Who knew that people would have been using spreadsheets on their tablets that long ago?

Rob Eastaway

The game of Diffy. A simple game with deep maths involved.

You start with a square and choose four numbers for the corners. He recommended picking ones between 0 and 30 to start with. I’m recklessly ignoring that advice.

Diffy1

Next find the differences between each corner and write that between them. Join these to make another square.

Diffy2

Continue doing this until you get down to zero and see how many squares you can get.

Diffy3

Once you’re at zero you stop. My choices of 8, 10, 50 48 leads to a total of only three squares. [I instantly wonder if the order matters.]

What’s the longest Diffy game you can find?

In completely unrelated news, (yeah, right) Rob introduced us to Tribonacci numbers:

1, 1, 1, 3, 5, 9, 17, 31, 57, …

Where each term is sum of the three previous terms. Apparently, there’s something interesting about the ratios of successive terms.

I love the simplicity of this game and the way it instantly makes me conjecture away. I also like the fact that I don’t think an algebraic attempt (call the corners a,b,c and d) is going to get too far.

And that was the end of session 2.

*Matt Parker’s vicious system for encouraging good time keeping is that if you exceed the allotted time, you’re subjected to Never Gonna Give You Up. It’s a brutal method but did keep people on track.

As usual, I welcome comments and corrections. I’m happy to link to the speakers’ twitter pages or web pages and also to link to presentations if possible.

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One Comment
  1. Stevie D permalink

    In answer to Michael Gibson’s question about the coin toss, using a brute force approach I can see the answer tending to 2/3, but I haven’t yet looked at working out why…

    In answer to Rob Eastaway’s the most I can get is 6 squares. It doesn’t seem to matter how big the numbers are, or even if they include fractions, negative numbers or even irrational numbers … by the sixth square all the numbers are the same. And yes, the order can make a difference.

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