# MathsJam Gathering 2020

This is a list of talks given at the 2020 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.

There is also a Cake page here with the photos of cakes entered in the cake competition.

The gathering took place on 21st - 22nd November 2020.

## SATURDAY

### SESSION 1

#### Alison Kiddle - Alison talks about mathematical origami

I've been doing lots of origami during lockdown, much of it mathematical. In this talk I will share some of the things I've made, and some of my musings, and show you how to make cool mathematical origami of your own.

#### Gavan Fantom - Approximating Simple Ratios with Irrational Numbers

We all know mathematicians like to approximate unwieldy values with nice simple integers and fractions. It turns out that it works both ways. But how? Why? Who even does this? What kind of perverse pleasure can be found in making the simplest of ratios more complicated? Stick around to find out!

#### Phil Ramsden - Ramsden's Bespoke Sliderules: Quality Craftsmanship Direct to the Trade

Before there were calculators, there were sliderules: physical devices that turned addition into multiplication. But not just multiplication. By making your sliderules bespoke, you can carry out any binary operation conjugate to addition under a real homeomorphism. That includes products, but it also includes parallel resistances in circuits, focal lengths of lenses, lengths of hypotenuses (in Euclidean and curved spaces), relativistic velocity sums...

#### Philipp Reinhard - Missing Pythagoras

Inspired by a painting from the Everything Is Number Exhibition, Philipp investigates triples that miss Pythagoras by 1 - and how you can generate them using Pell's Equation.

- Pell's Equation, on Wikipedia
- Everything Is Number Exhibition
- Philipp's slides (PDF)
- Philipp's slides (PPTM)

### SESSION 2

#### Miles Gould - Finding convex hulls with Graham's algorithm

Among the many giants that this ridiculous year has taken from us is the mathematician Ron Graham. He's best known for his work in discrete maths and in particular for Graham's Number, but he also worked in many other fields. I'll present his elegant 1972 algorithm for finding the convex hull of a 2D polygon.

#### Michael Borcherds - Factorising a quartic to prove something interesting about dice

First, Michael asks if you can factorise x⁴ + x² + 1 (into 2 quadratics, using integers). You can! Then using this Geogebra applet we see how to create a set of dice with the same probility distribution as normal 6-sided dice - using factors of a polynomial. You can change the sliders to rearrange the factors. (They're called Sicherman Dice!)

#### Belgin Seymenoglu - Number Munchers

Belgin gets hooked on a classic maths game - 1990s arithmetic eating classic Number Munchers.

#### James Arthur - Love: My insatiable desire to model everything.

A love life is difficult to handle and a lot to balance. It's a bit like having an egg and spoon balanced on your hand while trying to jump up and down repeatedly. James has always wanted to be able to understand a bit more about this and through Dynamical Systems has found an answer. In this talk James reveals the secrets uncovered by reading scholarly papers.

- Effects of random noise in a dynamical model of love (requires institutional sign-in)
- Dynamical Models of Love
- James' slides (PDF)

#### Gordon Hamilton - Mini Mathematical Universes

Inspired by some existing games, Mini Mathematical Universes are the best way to teach the scientific method. The audience will poke around like scientists and test their hypotheses about how each universe works.

- Patterns II by Sid Sackston
- Eleusis by Robert Abbott

### SESSION 3

#### Hannah Gray - Bridges & Banknotes

The bridges on the Euro bank notes used to be fictional, until someone decided they should really exist! Now you can visit the bridges in a Dutch town.

#### Alexander Bolton - The Element of Surprise

Some researchers came up with a strategy to beat state-of-the-art AI at a game by using a strategy that was not good but took the AI by surprise. I will discuss this game and how strategies that are bad but succeed because they are unexpected applies more generally.

- Adversarial Policies in Multi-Agent Settings
- Adversarial Policies: Attacking Deep Reinforcement Learning

#### Tiago Hirth - CIRM 1935/39

The first ever Recreational Mathematics meeting was held in Brussel followed by Paris. In tandem with the world fairs multiple mathematicians and maths enthusiasts gathered to exchange and have fun around and with maths ... sounds familiar? This is ongoing research in the History of Maths and I would love to exchange on the topic with others.

#### Pedro Freitas - Kepler and the Golden Ratio

The Golden Ratio has gained a special place among mathematical concepts, due to several non-mathematical meanings that it has gained through the years. In this talk we detail some of Kepler's views on the topic.

#### Douglas Butler - TSM Resources website - a major overhaul

I have been gathering material for my TSM Resources website for many years. This session will take you through the resources: useful images, excel-ready data, integer lists, Autograph files, video tutorials, general maths links, etc.

#### Francis Hunt - Navigating the Soma Cube map

Francis shares some hints on how to build a Soma cube, from John Conway et al.'s, and using the Somap.

### Saturday night tables

Among the activities people could participate in on Saturday evening were a Jeopardy! quiz run by the Chalkdust team, a live version of the Mathematical Objects podcast and a table playing Fractal tic tac toe, invented by Cesco Reale.

## SUNDAY

### SESSION 4

#### Sam Hartburn - Spirally Flowers

Beautiful graphs produced by a slight variation on the rhodonea curve.

#### Martin Whitworth - A method for solving quadratic equations

Martin presented the Carlyle Circle method for solving quadratic equations. To solve the equation x² - sx + p = 0, construct a circle with diameter (0,1),(s,p). The x intercepts are the roots of the equation.

#### Johnny Ball - Euclid

Johnny shares some of his favourite facts from Euclid, including some geometrical properties of lines in circles, and a way to find square roots uing a semicircle.

#### Peter Rowlett - nimsticks: making games with LaTeX and Lua

Nim is a game that involving picking sticks from piles. This talk briefly covered Nim, representing it in LaTeX and programming game solutions in LuaLaTeX.

- Peter's package for drawing Nim games, called nimsticks on CTAN

This provides commands \drawnimstick to draw a single nim stick and \nimgame which represents games of multi-pile Nim. Nim sticks are drawn with a little random wobble so they look 'thrown together' and not too regular. If you use MiKTeX then it should install itself. If you use TeXLive, then it is in TeXLive 2020, though you may need to update packages.

- The LuaLaTeX code for setting and solving Nim questions, available as nim-next-move on GitHub.
- Peter's slides (PDF)

#### Tony Mann - A favourite mathematical magic trick from Martin Gardner

Tony demonstrates a favourite mathematical magic trick from Martin Gardner's "Mathematics, Magic and Mystery" - in which a noughts and crosses game, with my opponent making free choices at each move, miraculously results in a magic square.

#### Matt Parker - Guess The Number of Dice in the Jar

Matt invites us all to guess how many dice are in a jar - but the jar isn't necessarily set up the way it appears to be. Lessons learned about mathematical modelling, and making assumptions!

### SESSION 5

#### Sophie Maclean - Puzzles and Polyominoes

A whistle-stop tour starting with the humble domino, and going all the way to infinity. Did you know Tetris was the first computer game played in space?

#### Adam Atkinson - Hamlet and Kepler

There is a game, possibly played by no-one, called Hamlet. In the maths version, you confess to not knowing or understanding things. Adam recently discovered that if he did ever play Hamlet he may now have a new candidate winning move involving Kepler's laws - in particular, that Kepler's second law applies to all central forces.

#### Jorge Nuno Silva - OULIPO: a Portuguese conspiracy

The literary movement OULIPO, created in the past century, has a forgotten Portuguese forerunner from early 19th century. An iconic OULIPO landmark - the book of sonnets Hundred Thousand Billion Poems - is predated by more than 100 years by JDR Costa's similar large collection of combinatorial poetry.

#### Martin Harris - An Unappreciated Result and a Folding Puzzle

A statement of an interesting result about the tangents of the angles of a triangle, and how this relates to a paper-folding puzzle.

#### Justin Roughley - Equatum: A Journey into the Unknown

Justin shares his Equatum puzzles, which involve filling in gaps in an equation or rearranging symbols to make a valid equation.

#### Colin Wright - A differently mutilated chessboard

Colin acknowledges the standard 'mutilated chessboard' problem, which involves moving two squares of the same colour so it can't be covered by dominoes. But if you remove one black and one white, can you make it un-coverable? It's possible to make an 8 by 8 chessboard un-coverable by removing three black and three white squares - can you find a way?

#### Christian Lawson-Perfect - Let's sort out this BODMAS nonsense once and for all

The BODMAS acronym for the order of operations is derided by many as "ambiguous", "hard to apply", and "not an acronym actually". Let's fix it.