# MathsJam Gathering 2015

This is a list of the talks given at the 2015 MathsJam conference, along with relevant links, and slides where we have them. There's also a page of photos from the baking contest here, and a Storify page of all the tweets from the weekend.

## Saturday

### Session 1a: 14.00-14.47

#### Welcome to the MathsJam, 2015 - Colin Wright

#### The geometrical dwellings of a Portuguese modernist - Pedro Freitas

Pedro showed us the work of Portuguese modernist artist Almada Negreiros, which draws heavily on geometric constructions.

#### Cumulative fairness - Phil Harvey

A pair of twins get the same pocket money, but in different weeks. How do you organise this fairly? Phil found the solution is a famous sequence!

#### Impossible Grilles - David Singmaster

While on holiday in Italy, David spends a large portion of his time looking at the iron grilles over windows. In particular, he looks out for this impossible-seeming pattern.

#### Coin tossing sequences - Martin Whitworth

Suppose you look for a particular sequences of heads and tails when you repeatedly toss a coin. How long should you expect to wait? If you're looking for two sequences, which should you expect to see first? Martin found a counter-intuitive answer.

#### Code Comfort - Pat Ashforth

Pat talked about codes of all sorts. The highlight was a knitted QR code.

#### Why waves wobble - Colin Wright

What do you get when you add two shifted sine functions together?

### Session 1b: 15.10 - 15.57

#### How to win football prediction leagues! - Michael Gibson

Michael doesn't know much about football, but that didn't stop him winning his wife's friend's dad's former colleague's football prediction league, using maths!

#### Magic, Maths and Gilbreath's principle - David Cushing

David showed us an amazing magic trick involving a simple riffle shuffle and a remarkable maths fact.

#### meta-Hnefatafl - Kathryn Taylor

Kathryn showed us a very old game played by Vikings. She tried to do some strategic analysis on it and found nothing interesting. Oh well!

- Tafl games online

#### Motorway Traffic: Shockwaves, Flow Breakdown and the problem of Hysteresis - Neal Harwood

Neal Harwood looks at traffic for a living. He showed us that shockwaves move backwards along roads at about 12mph.

#### Tetrahedrons made simple - Simon Bexfield

Simon Bexfield uses 3D printers to make tetrahedral puzzles - including a lovely shape called a Bathke, which can be joined in different ways.

#### DIY Calculating - Sam Headleand

Sam has been inspired by the Disco Calculator to build her own, using a Raspberry Pi and some Python code.

#### A paradox resolved? - Derek Couzens

Derek presents a little linguistic puzzle - if a heterological word is one which does not describe itself, is heterological a heterological word?

- Slides (PDF)
- Slides (PPTX)
- Grelling-Nelson Paradox, on Wikipedia

### Session 1c: 16.20 - 17.07

#### Dabbling with Dobble - Rob Eastaway

Rob's been playing the game of Dobble with his kids, and they've had a go at inventing their own version, which is similar to the process of constructing a magic square.

- Dobble, aka Spot-It!, at BoardGameGeek

#### Nim-like games - Peter Rowlett

Peter shares a few games which are similar to Nim, in which players take it in turns to choose a number of pieces from one or more piles.

#### What's in your purse? - Geoffrey Morley

Geoff takes us through some possible strategies for minimising the number of coins you might need to carry - if you're paying 64p, and you have a 5p and a £1 coin, handing over both will result in fewer coins in your change.

#### Regular Maps - Nick Wedd

Nick shows us some interesting maps on the surfaces of various manifolds.

- Slides (HTML) (further links in top right)

#### African Textiles - John Bibby

John investigates the mathematical shapes and patterns in African art and textiles.

#### The Samaritani Formula - Adam Atkinson

Adam asks: for which positive real numbers *a* does the power tower a^a^a^a... make sense, and explains how maths is used and abused in analysing the Italian lottery.

#### Our survey said... - Alison Kiddle

Alison has run an online survey of some mathematicians, and shares her interesting results.

### Session 1d: 17.30 - 18.40

#### G&P revisited, Eric Solomon's Hexagrams and more - John Read

John has been collecting old recreational mathematics magazines, and shows us a nice example of a set of hexagonal tiles which can be used to make interesting shapes. He's also baked biscuits of them.

#### Washing up after the potluck dinner - Alistair Bird

Alistair's puzzle is as follows: if all N people coming to a potluck dinner must bring a different number of portions of food, and each must bring at least N, how many different arrangements are there?

#### Droste Dobble - Christian Lawson-Perfect

Since Dobble, which has previously been mentioned by Rob, is based on a projective plane, where points and lines are equivalent, CLP has found a way to make a version of Dobble in which the symbols on the cards are replaced by Dobble cards themselves; Dobbleception occurs.

#### A Ring With A Fling To It - Elizabeth A. Williams

While riding a carousel on which riders have a chance to win a prize by throwing a metal ring from their moving horse into a stationary target, Elizabeth was inspired to analyse the maths and work out her optimal throw point.

#### On the Diffie-Hellman Key Exchange - Yuen Ng

Yuen explains this method of exchanging information securely.

- Diffie-Hellman, at Wolfram Mathworld

#### How to Set a Chalkdust Crossnumber - Matthew Scroggs

Matthew has been writing Crossnumber puzzles for Chalkdust Magazine. He explains his methods, and shows some interesting mathematics he's discovered in the process.

#### On bolts, and twiddling; Chella's dad's origami paper trick - Katie Steckles

Katie has brought along two large metal bolts so she can try for real Martin Gardner's 'Twiddled Bolts' puzzle; she also has an interesting origami trick which she hopes you haven't seen before, which involves wiggling an origami construction until a piece of paper reappears magically.

## Sunday

### Session 2a: 08.50 - 09.37

#### Conics and Co-ordinates - Ben Sparks

Ben introduces us to a way in which conic sections can be used to find lost aeroplanes, by finding the intersection of loci given some triangulation data.

#### HAFF Ellipsograph Nr. 97 - Michael Borcherds

Michael has been buying things on Ebay again, including an ellipsograph which translates linear motion into ellipse drawing.

#### Émilie du Châtelet - Nicholas Jackson

Nicholas introduces us to a little-known female mathematician, who worked with Voltaire and had a very interesting life!

#### Precision is a Stream - Andrew Macdonald

Andrew explains how we can use arithmetic encoding to communicate with aliens more efficiently.

- Slides (PDF)
- Arithmetic Encoding, on Wikipedia

#### The maths of chocolate fountains - Adam Townsend

Adam works with fluid dynamics, and chocolate is special in that it is a shear-thinning substance - becoming more fluid under shear stresses, which affects how it behaves. He also shows a nice way to demonstrate the inward slope of the fountain's curtain, using tap water, 10p and a pencil.

#### Six Matchstick Problems - Tiago Hirth

Tiago presents a selection of matchstick puzzles.

#### Magic Squares - Matt Parker

Matt reveals his latest obsession - magic squares - and points out some open questions in the area.

- Slides (PDF)
- Slides (PPT)
- Video: Matt's 4x4 Magic square method
- Multimagie.com, which includes a list of magic square types nobody's found yet

### Session 2b: 10.00 - 10.47

#### Sine curve sums: conclusion - Colin Wright and Martyn Parker

Colin and Martyn reveal the answer to the sine curves question posed the day before - if you add any two sine waves together, what do you get?

#### Cheating at MathsJam puzzles like a lazy computer scientist - Owen Cliffe

Owen was challenged to solve a Soma Cube puzzle, and did it the way any good computer scientist would - by cheating and writing a programme.

#### Lyness Cycles - Jonny Griffiths

Jonny describes sequences similar to Fibonacci, defined by a recurrence relation on the two previous terms, but which cycle through the same entries with a fixed period.

#### If I am telling the truth then I am king - Tony Mann

Tony illustrates a nice logical paradox, thus proving himself to be king. He also presents a related logical challenge involving two envelopes to a member of the audience, who has the chance to win a prize.

- Slides (PDF)
- Slides (PPTX)
- Curry's Paradox, on Wikipedia

#### My bike is awesome! - Rogério Martins

Rogério has a bicycle, which he can use to measure the area of a piece of paper - by rolling it along the perimeter like a planimeter. Compared to weighing the paper, which has a known weight per square metre, it's pretty accurate!

- Planimeter, on Wikipedia

#### The Braess Paradox - Ross Atkins

Ross presents a paradox about traffic - adding an extra route can sometimes actually increase the average journey time. Ross finishes with a demonstration using elastic bands, in which cutting one band caused a weight hanging from a system of elastic to actually move upwards!

#### 3D Printing From The Inside Out - Dan Hagon

Some mesh shapes are possible to 3D print, and others are not. Dan uses a bit of topology to figure out which.

### Session 2c: 11.15 - 11.48

#### A Pointless Talk - Phil Ramsden

Phil is a fan of TV quiz show Pointless, in which contestants are invited back if they have appeared in one previous episode without winning. How can we model this over a whole series? Using Markov chains!

#### Maths Bastard - Paul Taylor

Paul has invented a game which you play against a computer. Paul explains how it works. Can you beat it?

#### Curious and Interesting Triangles - Donald Bell

Donald has a puzzle which involves five identical 3-4-5 right-angled triangles. Can you arrange them into a shape which has mirror symmetry? Also, what makes a nice puzzle?

#### M500 and the overlapping triangles competition - Colin Aldridge

Colin's entry for the competition competition was a puzzle about overlapping triangle, and the solution surprised even him!

#### The Balls in the Barrel Problem - David Bedford

Infinitely many balls are taken out of and put into a barrel. Hilarity ensues.

#### Approximately Wrong - Tarim

Tarim illustrates a problem when determining geographical locations - as angles get smaller, their cosine tends to 1 and the number of degrees of precision you need increases.

#### Siteswap Juggling notation - Marcin Kowalczyk

Marcin shows off his juggling skills, using Siteswap mathematical juggling notation, and shows us a nifty juggling trick app.

- Siteswap Reddit page, with useful links
- iJuggle Siteswap app, on the Apple store

### Session 2d: 12.10 - 13.04

#### Presentation of maths magic - Simon Allen

Simon presents a few nice mathematical magic tricks.

- One of Simons' tricks, a Martin Gardner classic

#### Numbers are awesome - Josie Smith

Josie has discovered several fractions which appear to have infinite non-repeating decimal expansions... or do they?

#### Hannah's Granny's Humbugs - Ken McKelvie

Ken has extended the question of Hannah's sweets to a new version, about Hannah's Granny's humbugs.

#### Gaussian Machinations - Colin Beveridge

Colin has a cool fact about Gaussian integers.

#### Reciprocal Prime Magic Squares - Joel Haddley

Joel explains a fact about long division which also applies to magic squares.