# MathsJam Gathering 2017

This is a list of talks given at the 2017 MathsJam Weekend, along with a brief description, and links to slides or other relevant content where we have them. If you spot any mistakes on this page, or would like to update the description of your talk, use the 'Edit this page' link at the bottom with a GitHub account to propose changes and make a pull request.

There's also a Cake page here with the photos of cakes entered in the cake competition, and a PDF of the MathsJamJam Songbook from 2017.

## Saturday

### Session 1a: 14:00 - 14:47

#### Colin Wright, Matt Parker and Katie Steckles: Welcome to the MathsJam Gathering

#### Tom Button: All about the base (no trebles)

You might have heard that the square of a prime number (p>3) is always one more than a multiple of 24. Tom introduced the words *threven*, *throver* and *thrunder* for numbers of the form 3n, (3n + 1) and (3n - 1) respectively, and moved into dozenal, and suddenly the proof was easy.

#### Matt Peperell: Logical deduction games

Logical deduction games are those like Penultima, where players have to deduce the rules by being told when they've broken them.

Matt showed us a few of them, including Zendo, Mao and Eleusis which you can play with an incomplete deck of cards.

#### Alison Kiddle: Alison talks crap

Photo by Elizabeth @Realityminus3

Having seen the photo above, Alison wondered if the implied assumption about the number of 'sht's per 'sht' was accurate. She has gathered data about how the statistic differs depending on how you expand the abbreviaton 'sht' and how healthy you are, and presented her findings to us. She also delivers a fine array of puns which for various reasons will not be reproduced here.

#### TD Dang: The maths in Mean Girls

TD has watched *Mean Girls* which features a maths competition in the finale. She's put a lot of thought into not only how to approach the questions in it, but also how the wrong answers might have been arrived at.

#### Noel-Ann Bradshaw: Digesting the indigestible

Noel-Ann talked about different ways of presenting data. A highlight was her taking apart the commonly held idea that the y-axis must always include zero to stop a graph being misleading, by showing examples where that clearly makes no sense.

### Session 1b: 15:10 - 15:57

#### Zoe Griffiths: A discourse on e

Zoe impresively recites from memory a humorous poem she wrote about the base of the natural logarithm which told of the life of e.

#### Phil Chaffe: Maths Jammin' - Writing a song for the Maths Jam Jam

Phil gives us five tips on how to write a MathsJam song, in attempt to increase the number of entries for next year. So go on and give it a go!

#### Matthew Scroggs: Big Ben Strikes Again

Matt (Twitter) explains how in the Captain Scarlet episode "Big Ben Strikes Again", Captain Blue used real maths to calculate the location of a ~~bomb~~ civil device by correlating the rings of Big Ben he heard on Radio 4 with the rings he could hear from the clock itself.

#### Andrew Russell: Balloon Animals and Semi-Eulerian Graphs

Andrew shows us how every balloon animal should be a semi-Eulerian graph, but shows us an example of one that isn't, inviting us to work out how he's done it...

#### Angela Brett: Mathematical poetry

Angela recites a poem about how progress is made by standing on the shoulders of not only giants but a lot of shorter people too, and then shows us some Haiku that she discovered in mathematical texts using her own Haiku detector software.

- Angela's slides (PDF)
- Angela's 'Standing on the shoulders of Giants' poem, available to buy as a poster

#### Adam Townsend: Stop! (or, using maths to pass your driving test)

Adam (Twitter) avoids memorising stopping distances for his driving test by deriving and learning the equation instead, with justification from mechanics. Turns out the units you choose have a big impact on how memorable the formula is. Also, British people seem to believe that they have much faster reactions than citizens of any other country.

#### Elizabeth and Zeke: rat with an e

Elizabeth (and Zeke) talk (well, Zeke didn't talk) about tangent lines, what we should call them, and some flashes of intuition about what logarithms mean from a student with a different perspective.

### Session 1c: 16:20 - 17:07

#### Rob Eastaway: Thinking Outside the Outside of the Box

Rob presents some twists on an old classic puzzle - given a 3 by 3 square of dots, can you connect them all using four straight lines without taking your pen off the paper? He's extended it to 4 by 4 versions, and shows that there are plenty of possible solutions - some of which require thinking up to 133% outside the box...

Rob's tweet from earlier in the day

#### Rachel Wright: In A Spin

Rachel is interested in yarn, and showed us how the way spinning machines produce it - and an interesting topological puzzle it presented.

#### Alex Burlton: Bags of Palindromes

A palindromic number is one whose digits read the same backwards as forwards. Given a random collection of numbers, what's the probability you can arrange them into a palindrome, and how does this change as the number of possible digits changes?

#### Alexander Bolton: Winning the Chalkdust Coin Game

Alex describes a strategy for winning a game that involves flipping a number of coins, and using the number of heads and tails to determine your score.

#### Vincent Van Pelt: Thank you, Mrs Holcombe

Vincent has been investigating homophones - words which sound the same as each other. He's found quite an impressive list (the best one was 'Grothendieck K-Theory' which sounds like 'Growth and decay theory'.

### Session 1d: 17:30 - 18:17

#### Dan Hagon: Double Negation and the Excluded Middle

Dan talks about how asserting something is not the same as asserting the double negation of that thing, and how this can affect proofs by contradiction.

#### Ben Pace: Building Successful Intellectual Communities

Ben talks about the maths behind the PageRank algorithm, and how it can be applied towards trustworthiness scoring on social sharing sites.

#### Alison Clarke: Stupid Units

Alison (Alan) vents some frustration about numerous unit systems that make very little sense, and tells us a bit about how they came to be. Why is an acre not a square?

#### Belgin Seymenoglu: Donald in Mathmagic Land

Belgin shows us where some mathematical concepts from Disney's *Donald in Mathmagic Land* appear in the real world.

#### Douglas Buchanan: Lowering the Tone

Douglas gives us a puzzle and a pun:

"You are given 4 values. Using only the four simple operators, make 24. The four values are 3, 3, 8, and 8."

"I have fifteen parrots in a cage with three perches. When I clap, six parrots land at the bottom, five in the middle, and four at the top. How many do I own?"

*(six, the others are on higher perches)*

#### David Mitchell: The Theorem of Trithagoras (Pythagoras is for Squares)

David shows us a fascinating explanation of how you can multiply squares and triangles on the complex plane to find pythagorean triples and more.

#### Dave Gale: Catchphrase and Coffee

Dave presents some confusing coffee strength scales, and his increasingly formal correspondence with ITV over a misnamed quadrilateral in *Catchphrase*.

## Sunday

### Session 2a: 08:50 - 09:37

#### Joel Haddley: Angle Trisection

Joel shows us how to trisect angles in an infinite number of steps, although isn't sure if you can do this in a finite amount of time.

#### Katie Steckles: Sheeran Numbers

Katie makes 22262 different numbers using Number One albums as numbers and Ed Sheeran albums as operators, with a few constraints.

#### Ken McKelvie: A little ado about 'nothing'

Ken talks about where 0 appears in lots of numbers.

#### Tony Mann: The mathematics of competition

Tony finds yet another meaning of competition, and explains how having more ice cream vendors doesn't mean you have to walk less far to get an ice cream.

#### Will Kirkby: Life beyond binary

Will uses a trinary celluar automaton to sort binary numbers, then asks if you can use a (n+1)-ary celluar automaton to sort n-ary numbers, then finishes with some beautiful cellular automata with probabalistic values between 0 and 1!

#### Peter Rowlett: Fermi problems for teaching mathematical modelling

Peter uses Fermi problems he uses in teaching mathematical modelling. He also shares his favourite method for answering them, which is the *approximate geometric mean*, as described in this blog post.

#### Kathryn Taylor: Adventures in modular origami

Kathryn uses the visualiser to show us some incredible incredible origami shapes built from Sonobe modules - including one she's just invented and can't work out what it's called (it turns out it was a double stellated tetrahedron).

### Session 2b: 10:00 - 10:47

#### Marcin Konowalczyk: Unrolling the rolling shutter

Marcin talks about the rolling shutter effect which he's implemented in Python, and attempts to reverse-enginner while teaching himself neural networks.

#### Miles Gould: How Mountaineering is like Mathematics

Tips on how to find, finance, accomplish and document a new project, whether in maths research or climbing big hills.

#### Samuel Ball: Fake It Till You Make It

Creating new tweets from old ones using Markov chains, with the Twitter account of Donald Trump as a dataset.

#### Wendy Foad: Context vs content

Wendy talks about the importance of having a familiar context in problem solving, and the skills people have that they only use in one specific circumstance.

#### Nicholas Korpelainen: A production line may need an arbitrarily large number of machines

If you're running a production line, you could denote each machine by a letter A, B, C and list the order the machines occur along the line. If you want a given pair of machines to alternate (so as you go along the line, A doesn't occur twice without a B in between) you can create puzzles around how to arrange them.

For example, if A must alternate with B and A with C, but not necessarily B with C, you could loop the sequence A, B, C, A, C, B and this would satisfy both. You can draw a graph of the machines, with an edge joining pairs that are required to alternate. Nicholas shows that with more complex graphs (with the example of crown graphs, the number of machines you need in your sequence can be arbitrarily large!

#### Robert Woolley: Making board games fit - Numbers & Space

Rob has constructed a portable set of board game equipment that can be used to play a large variety of different games.

### Session 2c: 11:15 - 11:48

#### Glen Whitney: The Hole Truth

Glen reveals the results of his 'hole poll': he made some objects after dinner last night, one of which was shaped like a t-shirt (a hole at the bottom, one at the top, and two on the sides, all of which meet in the middle), and asked people to suggest how many holes it's actually got.

4 was the most popular response - perhaps, says Glen, this answer came about with 'proof by t-shirt' which says that because we have 4 things sticking out a t-shirt (similar to Glen's shape) it therefore has 4 holes.

Glen then uses Euler's formula, which suggests by analogy to the simply connected and toroidal cases that the object should have only three holes! With the help of some children's modelling putty, he concludes it actually does have only 3 holes and ends on a topology joke about steering wheels and t-shirts.

#### Sue de Pomerai: The life and times of Ada Lovelace

Fully dressed as Ada Lovelace (good effort!) Sue tells us about the life and work of Ada Loveace, including her work with Charles Babbage: noteably her translation of Babbage's paper about the difference engine where she brought out the Bernoulli Numbers, and made his paper less 'seriously wrong' and more 'beautiful'.

#### Pedro Freitas: A programmed deck

Pedro demonstrates a magic card trick - which involved him ordering the deck such that he could determine two integers an audience member was thinking of from their sum and difference. One to try at home!

- Some slides Pedro has made explaining the trick (PPTX)
- Some slides Pedro has made explaining the trick (PDF)

#### Matthew and John Bibby: Geometric tables and boring logs

Matt and John Bibby, whose title was a clever joke, show us items they have crafted together (including a truncated triangular based pyramid seat) and discuss how different mathematical patterns can be seen while boring a log to obtain a wooden bowl.

#### Geoff Morley: Irrational Bases

Geoff asks questions about irrational bases such as: 'What is 3 in base 2.6180339887....? He also asks questions and draws links between, amoungst others: Pisot numbers, negatives bases, and Ito-Sadahiro (-Beta)-expansions.

#### Adam Atkinson: Mathematics and Art: A Real-World Problem

Adam Atkinson tells us a 'real world maths story', which he defines as a conversation that 'occurs between two people who are not mathematicans'. A sculptor wants to install a sculpture on a mountain near Catania in Sicily, and Adam amuses us with the difficulties that he may incur. Notably, Adam calculates that to be seen at a decent size from the airport, it would need to be at least 200m tall, and Adam also conjectures it might have some competition from mother nature (the mountain in question is in fact Etna - one of the most active volcanoes in Europe).

### Session 2d: 12:06 - 12:39

#### Elaine Smith & Lynda Goldenberg: Multiplication: Magic or Madness

Elaine gives us a whistle-stop tour of different multiplication methods; including a refelction on the column method versus the Gelosia method, that draws on her experiences in the classroom.

#### Robert W. Vallin: Maverick Solitaire and Three-Card Poker

Robert discusses a couple of card games: Maverick Solitaire and Three-Card Poker. Robert tells us that by using a computer simulation it can be shown that a 'pat hand' can be made in Maverick Soilitaire a high proportion of the time. However, he conlcudes by asking us what percentage of the time we can get a straight flush in Three-Card Poker.

#### Robert Low: Why knot?

Rob explores mathematical knots, and explains how all manipulations can be carried out as a sequence of three Reidemeister moves, and demontrates how the colouring of different sections of the knot links to the solutions.

#### Philipp Reinhard: From a tweet to Landau's 4th problem in < 5min

Philipp spotted a riddle tweeted recently by one @ColintheMathmo, which asked can you find 'three integers in an arithmetic progression whose product is prime?'. He worked out that, when rephrased in the complex integers, this seemingly impossible puzzle boils down to 'How many numbers of the form n² + 1 are prime?'. This, Philipp tells us, is a famously unsolved problem.

#### Oliver Masters: The Fibonacci Matrix

Oliver shows three applications of the 'Fibonacci Matrix' (1, 1; 1, 0), including a suprising link between the Fibonacci Matrix and The Golden Ratio. Powers of this matrix contain only Fibonacci numbers, and when diagonalised a familiar face pops up...