# MathsJam Gathering 2023

This is a list of talks given at the 2023 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 2023. There is also a Cake page here with the photos of cakes entered in the cake competition.

The gathering took place on 11th - 12th November 2023.

### Session 1a 2pm-2.40pm:

#### Peter Rowlett: Am I related to Henry VIII's Master of the Mint? Are you?

Peter tried to work out how exponential growth applies to generations of a family, and whether this means he's likely to be related to the Rowlett who was Master of the Mint in Tudor times even though there's no documentary evidence of a family connection - and whether most other people in the UK are too!

#### Alyssa Burlton: MathsJam Presentation Presentation

What makes the perfect MathsJam talk? Armed with an anonymised dataset from last year and some rusty statistics, I attempt to find some answers.

#### Michael Gibson: A Talk You Will Either Love Or Hate

A woman has two children. One of them is a girl. What is the probability that the other one is a boy? What if, instead of being told "one of them is a girl", we are told "one of them is called Susan"? Does this change the answer? This "apparently simple" probability question has intrigued me for years, and has recently led me to consider a concept I will call "Marmitivity". I will share my thoughts on this with you in this thankfully brief talk. You will either love it or hate it!

After discussing what assumptions we are making before treating the problem mathematically, I showed some simple pictures to illustrate that the "classical" answers to these questions are 2/3 and 1/2 respectively. I then pointed out that, in answering the second question, we are assuming that girls are randomly allocated the name Susan with equal and independent probability. This ignores the fact that some parents will like the name Susan more than others. In the extreme case of the name Susan being ""like Marmite"", i.e. parents either love it or hate it, the answer returns to 2/3. More generally, the answer will lie somewhere between 1/2 and 2/3 depending on the "marmitivity" of the name Susan!"

#### Fredrik Kirkemo & Ida Soland Thu: The Rubik's Dice

We demonstrate a magic trick that uses a Rubik's cube, where all the squares have been assigned a number. The trick is related to magic tricks that us the fact that opposing sides of dice always sums to seven, allowing us to predict the opposing side of a die. We present the trick in two different varieties - one with a 3×3×3 and one with 2×2×2 Rubik's cube to show some of the mathematics behind the trick. The generalisation of the trick - or at least the 4×4×4 extension, will be presented as a hands-on exercise for people to ponder and fidget with during the rest of the Gathering.

#### Sam Hartburn: Ten to the Top, but Nine to the What?

Radio 2's morning music quiz has an interesting scoring system. I've analysed the possible scores to try to work out how fair it is.

### Session 1b 3.10pm-3.50pm:

#### Jørn Hafver: A(I) useless robot

Live training of an AI image recognition model. Using model to control a micro:bit that will trigger something amazing.

#### Ben Ashforth: Road Trip

How a talk at last year's MathsJam inspired Ben to complete a quest to find roads named after every day of the year.

#### Alison Kiddle: Guess who doesn't belong

A special version of 'Guess Who?' using 16 Disney Characters can be subdivided using four attributes so that each character is represented by a unique binary number from 0000 to 1111. A neat side effect of this is that we can easily pull out subsets of four characters to play "Which one doesn't belong", assuming the House of the Mouse doesn't pull us off stage for copyright violation...

#### Phil Ramsden: Sliderules II: the Kolmogorov Connection

Three years ago at MathsJam, I explored how, using a bespoke sliderule, you can calculate binary operations of the form S(x, y) = f^(-1)(f(x) + f(y)). It occurred to me a few months ago that if you take part of your sliderule and stretch it, a whole new set of binary operations becomes available. Unfortunately, I'm not the first person to have studied these operations. Fortunately, that person was Andrey Kolmogorov.

#### Daniel Johnson: From Numberblocks to Polyominoes

A look at how an episode of the heartwarming Cbeebies show Numberblocks touches upon the combinatorial concept of polyominoes. Using binary words we see how the number of polyominoes grows exponentially with size.

#### Tarim: Illogical Song Lyrics

Some song lyrics don't always make sense. Tarim played some clips of logically inconsistent pop tracks - from the lions in the mighty jungle, to the night when all the world's asleep - and we tried to spot the flaws.

### Session 1c 4.20pm-5pm:

#### Hugh Hunt: Pi Pong

You'll have maybe seen on youtube that pi can be computed by counting the number of collisions between unequal masses. This is an excellent video explainer, and here's an article by Colin Wright on the same subject. OK, it's fine in the maths but has anyone ever tried to do the experiment for real? Does it work? Well, it does! Here is a video of an experiment done on an air-hockey table. The mass ratio I have used here is 16:1 so that the number of collisions should be sqrt(16) × π which is exactly right - we observe 12 collisions!

#### Robin Houston: Simpler Substitution for Spectres

The world is abuzz with talk of new aperiodic monotiles: the hat and the spectre. I particularly like the spectre. The spectre paper explains how to understand the structure of spectre tilings in terms of a system of nine regular hexagons with marked edges. But this system is quite intimidating. It turns out you can actually do it with five: I’ll give a sketch of how that works, with lots of nice pictures.

#### Luna Kirkby: Buz: A Fizz Buzz Story

Luna presents a rapid-fire history lesson: What is Fizz Buzz? Some of Fizz Buzz's weirder variations, and Where did this Fizz Buzz thing come from anyway?

#### Donald Bell: Rectangling Squares and Rectangles

Can you tile a square with several rectangles that have no repeated side lengths? And can you tile TWO different rectangles with a set of rectangles that have no repeated side lengths? And can you make a nice multi-solution puzzle from rectangling rectangles?

#### David Hartburn: How to avoid zombies

Why is it difficult sometimes to avoid people on wide paths, when there is clearly space for everyone to pass?

#### Nessa Carson: Molecules that barely exist

Chemistry is driven by the release of energy and enthalpy (or chaos... very broadly speaking). Some of the most reactive organic chemistry works by reactively releasing strain within a molecule. This strain comes (again, broadly speaking) from electrons that are forced away from their geometrically-perfect orbitals. I'll be playing with Molymod kits that I think represent the geometries of molecules very well - just at 10^24 of their scale!

### Session 1d 5.30pm-6.10pm:

#### Sammie Buzzard: Spurious mathematical claims? How much of Antarctica is really penguin pee?

"3% of the ice in Antarctica's glaciers are penguin pee"- a claim I was made aware of at a previous Gathering, and one which I finally decided to use my glaciological and mathematical knowledge to put to the test.

#### Colin Graham: Know your place!

Many of you in England may have been exposed to a perculiary English activity known as "change ringing". This is mostly associated with churches in the Anglican faith, with some Episcopalian churches elsewhere in the world also being participants. There is a good deal of mathematics involved in how bells are rung in order to produce all of the possible combinations/permutations. Could you memorize 49,001,600 different combinations when only two pairs of bells can change position? I will tell you how it can be done!

#### Tom Briggs: Secret Histories: Spotting the Hidden Maths in Museums

The sum total of human mathematical knowledge didn't just pop into being last Thursday, but galleries, libraries, museums and archives have always been a bit shy about shedding light on its role in almost every part of history. This is a quickfire collection of just some of the gems I've seen sparkling through the cracks, along with a call-to-action for any museum-going maths fans.

#### Alexander Bolton: Abundant Numbers

Abundant numbers, e.g. 12, 60, 360, are useful as they have many factors. I will show how common these numbers are and how to find them.

## Sunday

### Session 2a 8.45am-9.30am:

#### Matt Parker: Calculating π by hand

Matt talks about plans to break the world record for most digits of pi calculated by hand. And how you can help!

#### Bob Huxley: When is Pi Day on Mars?

How does 3.14... relate to the Martian year? Unlike the Earth, the Martian year isn't naturally subdivided by the orbit period of a moon. Both Phobos and Deimos are tidally locked in the same area of the sky, to a Martian. And does pi = 3.14... on Mars?

#### Annette Margolis: Our preferred way of solving a quadratic is

I will be setting a quadratic to solve in class and each group will argue why their way is the best. The talk will be the results of this informal poll.

#### John Hoskinson: Beyond Diffy Squares

What happens if we apply the rules for Diffy Squares to other Polygons

#### Alistair Bird: Speaking truth to powers

In 1937, a mathematician suddenly leapt out of his mineral bath, rushed naked into the adjoining room, and began to scribble figures. We’ll talk about what he wrote, and what it can teach us.

#### Adam Atkinson: DOCTIAL

Adam recently needed to learn something about monoids and semigroups. One of the main things he learned was that there are an awful lot of them.

#### Harlan Connor: Winning the loudness war

I will show how some simple maths leads to some surprising (and loud!) results in signal processing.

### Session 2b 10.00am-10.45am:

#### Alex Arthur: A Sleepy German Village with an odd fountain

Alex explored a fountain in Rathaus, Germany. They showed some mathematical properties of the fountain.

#### Tony Mann: An amusing magic square

I will present an amusing magic square (at least, it amuses me)

#### Gavan Fantom: Meet the Flight Computer - a glorified slide rule

Although modern electronic tools are available for flight planning, pilots are still taught how to plan flights using a mechanical Flight Computer - a circular slide rule on one side, and an ingenious vector calculator on the other. Join me for a practical demonstration of this (nearly) century-old device and some of the calculations it can do quickly and efficiently.

#### Miles Gould: Surprising turns

A lathe is like a potter's wheel for wood or metal, allowing the user to create parts with circular symmetry about an axis. But by adding an extra spindle for a rotating cutting tool, it can be made to produce parts with *polygonal* cross-sections. How on earth do we get flat faces out of two rotating things? On closer inspection, it turns out the faces aren't truly flat: they're sections of a hypotrochoid curve, like those produced by a Spirograph toy. Hypotrochoids are part of a larger family of curves called roulettes, and several other roulette curves have industrial applications in machining.

#### Vanessa Madu: An Alternative Approach to Mathematical Modelling

There are lots of precise, rigorous, and inspired ways to construct a mathematical ocean model; I will not be talking about any of those. Instead, we will discuss a method born in the depths of my struggle to pull together my master’s dissertation; an alternative approach to mathematical modelling. Required: at least 4 rubber ducks (which will be provided) Optional: access to the North Pacific Ocean.

#### Joey Marianer: The True Prisoner's Dilemma

In "normal" versions of the Prisoner's Dilemma, the two players are (generally) humans with lives and families that we can identify with. This talk presents a modified version of the dilemma, where one of the actors is instead an evil/amoral AI which carries no (or even negative!) moral weight for most listeners. There is no difference in the game theory, though there is almost certainly a difference in how people react.

#### Andrew Taylor: Rotating an image without rotation

A demonstration of a graphic trick used by some old videogames, which manages to rotate an image using three shears. It's a lot faster than "real" rotation, and while it can look a little fuzzy, it has a couple of nice properties. It's reversible, and bijective — every pixel lands in exactly one place. This means some of them end up in slightly wrong places to make room for each other, and the result is a little jagged, but low-res rotation always is. In theory the maths says the rotation of the continuous coordinate space should be perfect, but the fact the pixels have to line up with the grid at every stage turns it into this bijective pixel rotation.

- Rotation With Three Shears - blog post by Tom Forsyth
- Rotation by Shears - Tobin Fricke
- Andrew's slides (web)

### Session 2c 11.15am-11.55am:

#### Matt Peperell: Showing off my curves

Most of us will be familiar with the conic sections and the trigonometric functions. In this talk, I will explain some of the lesser known curves and their uses in the world around us.

#### Pedro Freitas: A 19th century lottery - with a deck of cards

We present the workings of a lottery, conceived by a Portuguese scholar, Francisco Barba, from the early 19th century, that uses a deck of cards as a means of implementation. This is based on work done with Jorge Nuno Silva.

#### Ben Handley: How square is a circle?

Jay Foreman has a video (https://youtu.be/8mrNEVUuZdk) about finding the squarest country. But how can we judge the squareness of a shape? What happens when we try to find the squareness of a simple shape like a circle?

#### Clare Wallace: Skittles - Count the Rainbow?

Packaging says all sorts of nonsense: "it's not for girls", "only smarties have the answer", "every packet of Skittles is unique". They're all different kinds of wrong, but the Skittles one is the worst: it's *mathematically* wrong. Obviously we're going to work out how many different packets of Skittles there are. Obviously I've bought tons of Skittles. Obviously you'll get the chance to eat some.

### Session 2d 12.25pm-12.50pm:

#### Adam Townsend: Differential equations make pretty moving patterns (and now you can too)

When mathematicians want to talk about things that move and change, we talk about differential equations: heat spreading out in a room, sheep herds moving to fresh fields... Biologists have known for ages that when you have *two* competing populations both trying to spread out, the fun really starts. Modelling this was Alan Turing's day job, and what took him six months to compute, we can now do on our phones in real time. There are so many rich, pretty, dynamic, surprising patterns that you get from relatively straightforward equations and this last year I have been part of a team building VisualPDE.com: a website that instantly solves equations like this in the browser (think Desmos but for partial differential equations). In this talk I'll show you just how cool these solutions are.

- VisualPDE Simulation of the Heat Equation
- VisualPDE Simulation of a maze
- VisualPDE Simulation of Alan Turing's face

#### Hannah Gray: Gender in the Groove: Are Half Our Tunes Topped by Dudes?

An off-hand comment when playing Heardle led to an investigation into whether 50% of songs are sung by men.

#### Colin Wright: The Moebius Rollercoaster

Some rollercoaster rides are described as "Moebius" ... where's the twist?