# MathsJam Gathering 2012

This is a list of the talks presented at the 2012 conference, along with slides where we have them. If you'd like to send us your slides, or more detail about your talk, please email manchester@mathsjam.com.

The gathering took place on 17th-18th November 2012.

## Saturday

### Session 1

#### Why teens want to learn maths - Jeremy Renals

Jeremy discusses the idea of teaching mathematics to teenagers, and the challenges this presents - inspired by a TED talk, which says to give students autonomy, mastery and purpose.

#### How To Improve Your A Level Results - Phil Harvey

Phil tells us about Simpson's Paradox - by analysing different subsets of a dataset, you can alter the statistical conclusions and make your results appear to go up, even if they go down when you look at the full data set! Phil discusses A Level results and cricket scores.

#### On fair partitions of {1,2,...,n} - Ray Hill

Ray talks about work he did to generalise a problem to do with subsets of sets of numbers posed by Phil Harvey at the 2011 MathsJam. Can you partition the set {1, 2, ..., n} into 2 subsets such that the sums of the *t*^{th} powers of their elements are the same, for lots of values of *t*?

#### Unexpected expectations in coin tossings - Mark Holland

Mark describes Penney's Game, in which it's possible to sway the odds in your favour by choosing the right combinations of coin tosses. Also: how long should it be before we see three heads in a row, or two heads then two tails?

#### The Swearing Graph - Micky Bullock

Micky has discovered some graphs which make strange shapes when you vary the parameters - including one which sticks two fingers up at you!

- The Swearing Graph on Micky's blog

#### Rulers, ropes and telescopes - Alistair Bird

Starting with a challenge he was given by a bargeman wanting to have a set of ropes he could tie together to make as many different lengths as possible, Alistair talks about the unexpected link between the Golomb ruler, which has the minimum number of markings so that you can measure any integer length, and the Sidon sequence, a set of number whose pairwise sums are all different.

#### n interesting things about pi(e) - Kathryn Taylor

Kathryn tells us a non-specific number of interesting facts about the circle constant.

#### n things you can do with a sheet of squared paper - Alison Kiddle

Ending the session, Alison had us all drawing on squared paper, doing puzzles with digits, L-triominoes, reptilings & perimeters.

### Session 2

#### Why a capella singers go flat... or not! - Colin Graham

"Warning: this presentation may contain Mongolian throat singing." Not a phrase you normally hear at a maths conference! Colin introduced us to the ratios of frequencies involved in harmonics, and the mathematics involved!

#### The Game That Plays Itself - Clare Sudbury

Clare tells us about the card game Beggar-My-Neighbour, in which each player's next move is dictated by the cards just played. While the game itself is determined fully by the shuffle of the deck, Clare has written a programme which simulates the game being played repeatedly, to see what the chances are of it terminating after a certain number of moves.

#### Barely average wins GOLD - Michael Carding

Inspired by the Olympics, Michael answers the questions, "How good can you be and still only win silver?" and, "How bad can you be and still win gold?

#### Galois wipes the smile off Kate Middleton - Selwyn van Zeller

Selwyn shows us a trick which combines the Thatcher effect and the "two arrows point in four directions" trick to confuse us all!

#### Everything You Always Wanted to Know About Hex But Were Afraid to Ask - Noel-Ann Bradshaw

Noel-Ann talks about a boardgame invented by John Nash which she plays at Greenwich University Maths Arcade.

#### Maths-World UK: the new UK Maths Museum - John Bibby

John tells us about the plans for a new Maths Museum in the UK, as well as inviting us to contribute suggestions for exhibit content, potential locations, and funding sources.

#### Build your own electric motor - Yuen Ng

Yuen presents a simple way to make a motor using only a battery, a nail and a bit of wire. It really spins!

#### What shapes can you makes from equilateral triangles? - Michael Borcherds

Michael shows us some shapes made from equilateral triangles, including Lobel Frames, which are surprisingly rigid structures invented by French architect Alain Lobel.

#### Mathematics puzzles: four colours on a cube - James Eadon

James has created a toy called *Culica* which involves making patterns on a cube using pegs.

### Session 3

#### Domino computing - Matt Parker

Matt describes his recent ridiculous computing project in which he built a 4-digit binary adder entirely from domino chains, and shows us a video of the computer in action.

#### 100823 - Clive Tooth

Clive talks about his lifelong quest to find the least power of 2 having exactly n consecutive zeroes in its decimal representation, for each n, and his experiences breaking various large computing devices while seeking it.

- The least power of 2 having exactly n consecutive zeroes in its decimal representation at the Online Encyclopedia of Integer Sequences

#### How to Build a Pyramid - Elizabeth Hind

Liz Hind dispels the myth that the Egyptians used the 3-4-5 triangle in building the pyramid. No slaves used either!

#### The ant and the rubber band - David Bedford

Every ant has an arch-nemesis with a very stretchy rubber band but it can be beaten, says David Bedford. Proof by MathsJam!

#### Platonic Skeletons - Donald Bell

In skeleton cubes, as in life, some mate with their opposites, and some mate with those like them. Donald talks about a burr puzzle based on the 'skeletons' of platonic solids.

#### Preliminary investigations of a large dataset - Peter Rowlett

Peter gave his students the task of finding statistical interest in huge datasets, such as tweets around the Olympics.

#### Theory of Mind - Tarim

Tarim talks about the famous "blue-eyed islanders" problem, and its solution involving the islander's theory of mind - if you know someone else knows something, what can you deduce?

#### The game of Dobble - Martin Whitworth

Martin describes a French card game with an interesting combinatoric property - each card has seven symbols on it, and every pair of cards has exactly one symbol in common.

#### Schr�dinger's 2-box problem - Tony Mann

Tony describes a probability game with a paradoxical result, and a related "proof" that the probability a random integer is divisible by 7 is ½

#### Monthly MathsJams Annual Report - Katie Steckles

Katie presents data from the growth in monthly MathsJams, as well as thanking all the organisers and calling for new MathsJams to be set up.

## Sunday

### Session 1

#### A load of balls - Hugh Hunt

Hugh demonstrates an extraordinary fact: a ball bouncing under a table will come back almost exactly the same way it came.

#### Asexual rabbits in Lineland - Robin Houston

You might already know that the reproduction of rabbits gives a Fibonacci number of breeding pairs in each generation; Robin has noted that a line of slope ϕ on a square grid will cross horizontal and vertical lines in a pattern which lines up nicely with the number of adult and baby rabbits at each stage!

#### Doubling Hypercuboids - Joel Haddley

Starting with a rectangle made of square units, if adding a layer of squares around the outside doubles the number of squares, it's called a doubling rectangle. Can we find equivalent objects in more than two dimensions?

#### Forming the Ice at Parties with IPv4 - Adam Atkinson

Adam tells an amusing anecdote about a perplexing tech support call he once got, which turned out to be the result of there being several overlapping ways of writing IPv4 addresses.

#### Paradoxes or What we do in Portugal - Tiago Hirth

Tiago shows us a card trick that uses De Bruijn sequences, and then tells us about two conferences we should go to!

#### Poincaré dodecahedral space - Nicholas Jackson

Nicholas tells us about the Poincaré dodecahedral space, and how we may be living in one!

#### Raspberry Pi - the £30 Computer - Ben Nuttall

Ben tells us all about the cheap, simple computer that's gaining popularity and helping lots of people learn to program.

#### Turing, Colouring, and NP-Complete - Colin Wright

Colin invites us all to colour in some simple graphs, but without realising it we've created an AND gate! He can use a similar method to factorise large numbers and solve NP-complete problems.

#### What do imaginary roots of quadratics look like? - David Wilson

David wonders if it's possible to plot the imaginary roots of a quadratic, and discovers the 'evil twin' of the *x*^{2} graph.

### Session 2

#### Towards a set of non-non-transitive dice - Paul Taylor

Inspired by James Grime's Grime Dice, Paul has created a set of dice which aren't non-transitive, but using the non-transitive relationships between rock paper & scissors to populate the faces.

#### Understanding means - Ken McKelvie

Ken discusses the difference between knowing and understanding.

#### Needle Cars - Francis Hunt

Francis makes a reasonable assumption about automobiles - that they have negligible width - and proves that you can turn aroud in an arbitrarily small space.

#### An interesting, but wrong, solution to the birthday paradox - Colin Beveridge

#### Radius of a cube - Tom Button

What does the term 'radius' mean for an object other than a sphere? Tom describes some alternative definitions.

#### WOW cards - Mark Carney

Mark has created lots of 'impossible' shapes by cutting playing cards and weaving them together in ways which seem to contradict the laws of physics! He lets us see some of his creations, including an entire deck of cards which has been placed intact inside a glass wine bottle.

#### What you see isn't necessarily what you get - Steve Plummer

Steve shows us an image in which you may see different things depending on your point of view, and describes how he uses it to introduce non-mathematicians to some mathematical thinking.

#### SURDS! Huh! Yeah! What is it good for? - John Read

John Read invites a discussion on whether teaching surds is worthwhile, and whether they have any real practical applications.

#### Hark, the Mathematicians Sing - Elizabeth A. Williams

Elizabeth has rewritten the words to several more Christmas carols to give them a mathematical flavour, and invites us all to join in with a singalong.

### Session 3

#### How to 'simply' square 'any' rectangle - Geoffrey Morley

Geoffrey describes methods for dividing a rectangle into squares - he can use just 12 sizes of square tile to build rectangles in any proportion containing no sub-rectangles.

#### MathsJam Gets Deranged - James Grime

James talks about derangements - permuations in which none of the items remain in their original position - by analogy with both hat-wearing and swingers parties.

#### Classifying Surfaces - Miles Gould

Miles talks about the Euler characteristic of a surface (and shows off his snazzy topological knitwear).

#### My favourite maths book - Christian Perfect

Christian talks about his favourite maths book: an arithmetic textbook from 1811 that he bought at his local market.

#### Red Letters and Golden Numbers - Christopher Hext

Christopher describes the method he learnt as a child for determining the date of Easter given the date of the vernal equinox.

#### The Duckworth/Lewis Method - Andrew Taylor

Andrew teaches us the famous mathematical formula used for determining the outcome of curtailed cricket matches.

#### Wears the Maths - Pat Ashforth

Pat shows us some of the mathematical knitted items she has brought, including wall hangings that show different images when looked at from different angles, and a jumper made from two Mobius strips.

#### Controlling the Cost of Loving - Phil Ramsden

Phil Ramsden presents comedian Richard Herring with a more sensible solution to his romantic predicament - he bought his girlfriend one, two, four and eight Fererro Rocher in consecutive years, but is now doomed to an exponentially expensive gift: but Phil has found another function which fits those values and doesn't grow as quickly!