# MathsJam Gathering 2019

This is a list of talks given at the 2019 MathsJam Gathering, 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.

Andrew Taylor has produced a poster of the things that happened at MathsJam 2019. There is also a Cake page here with the photos of cakes entered in the cake competition, and a PDF of the MathsJamJam Songbook from 2019.

The gathering took place on 30th November - 1st December 2019.

## SATURDAY

### SESSION 1a

#### Adam Townsend: Mathematical socks: A review

Maybe you also receive maths-themed socks for Christmas. In this walkthrough, I com-pair and rank the most popular maths for socks, and try to rev-heel who designs these in the first place... no mean feet.

#### Belgin Seymenoglu: Math Blaster

Belgin plays a classic mathsy game from her childhood... in 16-bit graphics! Here’s her review...

#### Daniele Aurelio: The actual Library of Babel

Musings on pi, cryptic (in)finite libraries and how sticks can become books.

#### Rachel Wright: A problem of (inadvertent) pattern making

An unexpected problem of patternmaking, and the even more unexpected use of that same characteristic...

#### Adam Atkinson: Roman Mathematics

Some countries are unmixed - mixed numbers don't exist, or are perceived not to exist. Adam talked about Italy as a specific example since he knows it better than the others he has heard of (France, Spain, Portugal). The talk was partly about unmixedness but mostly about how hard it is to investigate this kind of issue. If you work with people from overseas it could be useful to know that some of them may never have seen mixed numbers before.

- Adam's slides (PDF)
- The 2018 article Adam referred to; some of the reactions, and some other reactions

#### Geoff Morley: Neosemimagic Tilings

A generalisation of both semimagic squares and perfect squared squares brings new challenges.

#### Laurence O'Toole: Predicting Groupthink - A Magic Trick

Make a prediction, and deal out several number cards to the audience. Then play a simple 2-rule game, where people take turns in picking one of the remaining numbers. Afterwards, all of the choices match the original prediction in a nice way.

(I'm not sure if I'm explaining this terribly well. But I don't want to just explicitly write out the details of every single step of the trick. I have no objections if anybody wants to rewrite the above paragraph after the fact.)

### SESSION 1b

#### Peter Rowlett: #tmwyk

#tmwyk is a Twitter hashtag used to share mathematical conversations with children. I will share some examples of mathematical chat I’ve had with my four-year-old and touch briefly on play in mathematical education.

- Peter's slides (PDF) - mostly just photos
- The #tmwyk hashtag
- A blog post Peter wrote about this

#### Tony Mann: A curious magic square trick

I recently came across this interesting variation of the 'I will construct a magic square for a given target sum' trick, due to Andi Gladwin and published as Magic Squared, by Vanishing Magic.

#### Mark Fisher: Mersenne and Cole

Cole found the factors of 2^67 - 1, after Mersenne had claimed it was prime

- Mark's slides (PPT)
- Mark's slides (PDF)
- More information about Mersenne and Cole

#### Eva Lesny: How many are in a few?

What do 'a few', 'a handful', and 'almost' mean to you? Ever wondered if they mean the same to others?

#### David Mitchell: The Brothers Fibonacci; Etiam mingens mathematicae memini!

Shyness in the gents pointed Fibonacci to his celebrated discovery. Even greater shyness leads to a generalisation of his sequence and of the algebraically expressible Golden Ratio to which the ratio of successive numbers converges. (Thanks to Nottingham MathsJam attendees for illuminating observations)

#### Claire Cohen: Exploring shapes with Curvahedra

Some interesting topology and shapes made with Curvahedra.

#### Alaric Stephen: Rational Origami

Starting with a unit square of paper, how can we fold it to divide a side into a ratio of 1:2? How about 3:4? In this talk we will explore a method for producing any rational ratio using a minimal number of folds.

#### James Grime: S.O.X.

James presents one of his favourite mathematical books - and he's written his own version and gives everyone a copy!

### SESSION 1c

#### Tom Button: Is the mathematical mind flat?

Do we solve mathematical problems subconsciously or is this just a myth?

- Tom's slides (PDF)
- The book which inspired Tom's talk, The Mind is Flat by Nick Chater

#### Sam Hartburn: (Not) Squaring the Circle

A poetic (well, rhyming (well, mostly)) look at some shapes that can be squared using ruler and compass.

#### Alexander Bolton: Factor Graphs and Unsupervised Joke Generation

I will introduce the concept of factor graphs and describe an application of them to joke generation.

#### Jonathan Welton: Domino Knights and Patios

If chess pieces were domino sized, what move would the knight have? And what boards could it tour? And just what has this to do with garden design?

#### Martin Chlond: The Travelling Salesman Problem: A couple of whimsical applications (Part 2)

Completion of last years talk.

#### Alistair Bird: The Bottle Imp

The Robert Louis Stevenson short story The Bottle Imp has an unusually mathematical set-up, with an inductive quandary like the 'unexpected hanging' or 'surprise exam' paradox. We also talk about a card game based on the story, and discuss how to behave before an apocalypse.

#### Karen Hancock: How many ways to turn a corner?

Thoughts on the many variations of a sock heel.

#### Yuen Ng: Moving on from Napier's bones...

A brief demo of some Genaille-Lucas rulers - does bigger always mean better?

### SESSION 1d

#### Rob Eastaway: Jardin's Principle

Jardin's Principle states that the road to full understanding passes through three stages: simplistic, complicated and finally simple. It's hard to get to the final stage without going through the other two first - and most of us get no further than stage 2.

#### Hannah Gray: Escher in the Palace

A very brief introduction to Escher's work and the permanent exhibition in The Hague (my new home!).

#### Gavan Fantom: What if numbers could have negative digits?

Imagine if individual digits within a number could be either positive or negative. Could you use small negative digits instead of large positive ones? Could you avoid learning your times tables past five? Join me for a brief introduction to a fascinating approach to arithmetic.

- Gavan's slides (4x3) (PPT)
- Gavan's slides (4x3) (PDF)
- Gavan's slides (16x9) (PPT)
- Gavan's slides (16x9) (PDF)

#### Martin Whitworth: Sums of powers

I guess most Mathsjammers know the formula for sums of consecutive integers, and many may know the one for sums of squares, but what about higher powers? - and how is Pascal's triangle involved?

#### Elaine Smith: Chinese Take-Away!

Discussion on several Subtraction techniques, including 'borrowing and paying back' (milk-bottle method); decomposition; invisible number line.

### SESSION 2a

#### Colin Wright: 70 vs 100

We all know that if you're travelling faster it takes longer to stop, and we think we know the rules. But do we?

#### Matthew Scroggs: Why and how I wrote a LaTeX package

In early 2019, I wrote the realhats LaTeX package with Adam Townsend. This package redefines \hat to put a picture of an actual hat on a symbol instead of a ^ hat. Because why not.

- Matthew's slides (PDF)
- RealHats website
- RealHats on CTAN
- RealHats on GitHub
- Aperiodical post about RealHats

#### Pat Ashforth: Using maths without knowing it

How to persuade knitters and crocheters to use maths without knowing it

#### Matt Peperell: An unexpected use for the golden ratio

It's not just pentagons and fibonacci!

#### Isabel Coelho: The Mirror Reversal Problem

I look in the mirror. My reflection looks back at me. When I wave my right hand, my image waves her left. When I wave my left hand, my image waves her right. Why do mirrors reversal left and right? And, if right becomes left and left becomes right, why does not top become bottom?

### SESSION 2b

#### Hugh Hunt: Bending vibration of a beam - nodal points and modes

Hugh share a beautiful - and musical - demo to do with vibration of a beam, and how this helps if you have a noisy washing machine.

#### Alison Eves: Florence Nightingale: the compassionate statistician

2020 is the bicentenary of Florence's birth: a great opportunity to celebrate her contribution to statistics, and their use in saving lives!

#### Andrew Taylor: The Belt Trick Spinor

I saw a GIF of this lovely belt trick spinor on Twitter and wanted to understand it, so I built my own version.

What's actually happening is that the central cube is always drawn upside-down, but the *axis it's rotated about* is spinning. The rotated cube in the final scene spins twice as fast as the axis — but once the axis has rotated 180º and the cube is back where it started, the space around it (and therefore the connecting belts) is stuck interpolating the other way. You need to rotate the axis another 180º to reset the whole scene, and that's where the 720º periodicity comes from.

-GitHub repo of the normal spinor -The double version

#### Christian Lawson-Perfect: Baked Sudoku

You can impose on Sudoku puzzles a physical system which works surprisingly well. It has phase transitions, and when you reduce the heat it settles into a solved state!

#### Miguel Gonçalves: From a new deck to Si Stebbins

How to prepare a Si Stebbins stack from a new deck order during a performance.

#### Stefania Delprete: Why the music staff is not really mathematically correct?

Last year I started an in-depth course on Jazz Harmony. A lot of new concept for my ears and eyes: major and minor chords, harmonized scales, and so on. Even if my teacher, and impressive pianist, told me I was making my life more difficult, I needed to create my own version of the musical staff, in order to use simple Maths instead keep memorizing notes positions and combination. I call it 'super-penta' (the staff is called 'pentagramma' in Italian) and you can use it too!

### SESSION 2c

#### Scott Elliott: Modulating secondary waves into screw threads

Deux Nuts is a tricky bolt with two captive nuts that mysteriously twist opposite directions on the same screw thread. How? Scott graphically illustrates the maths of its construction. Step by step, Scott overlays sin(-2𝛩) atop the peaks of a conventional screw-thread to make an unconventional nut go the wrong way.

#### Sydney Weaver: Permutations of the Cube

Discussing approaches to calculating the permutations of a rubik's cube and other twisty puzzles.

#### Miles Gould: Quantum computing in perspective

In quantum computers, the state of a qubit (quantum bit) can be something in-between 0 and 1 - but in what sense in-between? They're not elements of the interval [0, 1], but it turns out that there is a natural geometry for the state space of qubits: *complex projective space*, closely related to the mathematics of perspective drawing.

#### Zoe Griffiths : Two thousand and nineteen

Zoe performs a mathematical trick that she designed after reminiscing about key mathematical events of the year 2019.

#### Luna Kirkby: Cursed Regular Expressions

We explore the equivalence between regular expressions and finite state machines, and discuss how to reduce any FSM into a regex, culminating in some truly cursed behemoth regular expressions based on sokoban, peg solitaire, and even juggling.

#### Lucy Rycroft-Smith: Ten New Maths Jokes

Most maths jokes are terrible. It's time for some brand new ones...

### SESSION 2d

#### Alison Kiddle: Adventures with Dodecahedra

Dodecahedra are pretty cool! In this talk, I will share some of my favourite dodecahedral things you can make and do.

#### Louise Mabbs: Circling the Square & my Mathematical Magic progressions

Louise demonstrates a selection of mathematical quilts, based on rainbows and polar coordinates giving beautiful circle and spiral shapes.

#### Gordon Hayes: How to Avoid a Hangover Using Maths

A little graph theory. This talk will probably give you a hangover instead of helping you avoid one. On the other hand, everyone loves a bit of graph theory!

#### Tarim : Horseshoe Orbits

Why do the planets and moons in the solar system all spin in the same direction (mostly)? And what does this have to do with the stranger motions of two of the moons of Saturn?