# MathsJam Gathering 2022

This is a list of talks given at the 2022 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 19th - 20th November 2022.

## SATURDAY

#### Colin & team: Welcome to MathsJam

Welcome to the day.

#### Zoe Griffiths: The Great Collatz Collab

Zoe talks about the process of making a poster of a giant Collatz map made from snippets of hundreds of other maps drawn by school students.

#### John Bibby: Is 2023 a Prime Number?

How can 2023 be used as a seed for introducing non-mathematicians to the uses of prime numbers? This is a dummy run for a 30-minute talk in January to my local U3A, so I would welcome suggestions regarding further ideas to include.

#### Alistair Bird: Inequalities and inflation measures

We'll talk about how inflation is measured via the Retail and Consumer Price indices (RPI and CPI) and how a the Arithmetic-Geometric mean inequality is important to understanding the difference between them.

#### Christian Lawson-Perfect: Talk talk talk talk talk choo choo!

Five talks about the maths of trains. I'll warn you that I know a lot more about maths than I know about trains!

#### Colin Graham: Size isn't everything!

Why is A4 called A4? I will be looking at why we have the current standard paper sizes.

#### Mark Fisher: Dealing with Liar's Dice

A look at some fun variants of Liar's Dice using playing cards instead

#### Sam Hartburn: Icosahedral Ocarinas

I'll show you how to make an icosahedral ocarina out of cardboard.

### SESSION 1b

#### Sydney Weaver: Math Is Hard, Can we make it Easier?

Sydney will demonstrate through a variety of methods why math is hard sometimes and what we can do to potentially make it a little bit easier.

#### Mike Frost: George Abell and the End of Humanity

George Ogden Abell (1927-1983) was a distinguished American astronomer and much-respected educator. In his 1978 textbook "The Drama of the Universe" he proved mathematically that mankind could not continue to exist beyond 20th August 2023. Assuming he's not correct (and a few months late with his prediction), I'll explain why I think his analysis was wrong.

#### Miles Gould: Tactical Unruly

Last year I got badly addicted to the puzzle game Unruly, also known as Takuzu, Binairo, or Sudoku Binary. But after a while I noticed that only a handful of tactics seemed to be necessary. Was that limitation real, or was it possible to construct harder puzzles?

#### Colin Wright: When it's pippish, sides don't matter

When playing backgammon it's occasionally necessary to calculate who's ahead in the running. There are a lot of techniques for doing this, but a surprising result can make it easier than expected.

#### Sophie Maclean: Do the Dougie

Your Dougie Day is the day on which your age, in days, is the same as your date of birth!

#### Alison Kiddle: GeoGebra One-liners

What's the most interesting thing that can be drawn in GeoGebra using just one line of code in the Input Bar?

#### Dave Budd: Absurd Proofs

There are so many ways to geometrically construct the golden ratio with ruler and compass. Given the golden ratio is defined in a geometrical way, we should be able to prove geometrically without using surds that a construction is golden just by using geometry too, right?

#### Tony Mann: Good and bad luck in maths

Like everything else in life, mathematics is affected by luck. I'll give a examples of good and bad luck in mathematical discoveries and careers, including describing how one student was particularly unlucky in their degree final year maths exam.

### SESSION 1c

#### Belgin Seymenoglu: The Wi-Fi integral: no integration required

In 2018, a Chinese university canteen left a tough-looking integral that went viral on the net. Students wanting the Wi-Fi password needed to solve it and enter the first eight digits of the answer. However, it turns out you don't have to do any integration to solve it - just some easy symmetry arguments will do the trick. The final answer looks like a very familiar number...

#### Peter Rowlett: On-Sets: a vintage game of set theory

On-Sets is a game designed in the mid 1960s to teach set theory and has some cool dice. I’ll talk about the game and some puzzles that arise from it, and bring a set you can have a play with.

#### Paul Kennedy: Clapping Music – a music lesson and some counting

Steve Reich’s Clapping Music, is a (very simple) cyclic permutation. Using necklace polynomials it is possible to calculate both the number of possible clapping musics and the number of clapping musics of length n. The prime case is trivial. Further, a Lyndon word is hidden in Clapping Music.

#### Philipp Reinhard: Graphs for divisibility rules

We explore how directed graphs provide divisibility rules, also for the number 7 or whatever your favourite number happens to be. And it will work in any base. The graphs turn out to be rather beautiful and quite similar to fractals.

#### Hannah Gray: Arithmeum: fun with calculating machines

I accidentally found another fun and mathematically interesting place to visit so this is a quick guide to the Arithmmeum in Bonn.

#### Michael Gibson: The Joy of Six

Assuming everything went to plan... I tackled some problems, the main two of which were apparently very complicated and challenging, very quickly and easily by casting them on grids divided into six. The conclusion is that, due to 2 and 3 cropping up more than any other numbers, basing things around the number 6 will often avoid the need to grapple with fractions.

#### Colin Beveridge: A Pair of Puzzles

Colin shares a two puzzles about flapjacks and resistors, which turn out to be equivalent to Mrs Perkins' Quilt and Squaring the Square.

#### Phil Ramsden: Fun With Digit Sums

Let’s pick a positive integer; say 19. In base 2, its digits are 10011, and their sum is 3. Let’s note down the difference between the number and its digit sum, divided by one less than the base; this is (19-3)/(2-1) = 16. In base 3, we’ve got 201, and the digit sum is still 3. This time, (19-3)/(3-1)=8.

We’ll skip base 4, because only prime bases concern us here. In base 5, 19 is written as 34; the digit sum is 7, and we have (19-7)/(5-1)=3. In base 7, 19 is 25; the digit sum is 7 again, and (19-7)/(7-1) = 2. In base 11, we have 18, giving digit sum 9: (19-9)/(11-1) = 1. We get 1 in bases 13, 17 and 19, as well, and zero after that; you can check this yourself!

The first thing to notice is that we always get an integer answer. The second thing is that these aren’t just any integers; if we raise the bases to these powers and multiply, we get 2^16 × 3^8 × 5^5 × 7^2 × 11 × 13 × 17 × 19, which comes to 121645100408832000. Now, it just so happens that 121645100408832000 is equal to 19 factorial.

This always works. What might a proof look like, though? And is there a “digit sums” formula for powers in prime factorisations of numbers that *aren’t* factorials? (Hint: yes.)

### SESSION 1d

#### Eliza Gallagher & Neil Calkin: Ordering Chaos: Bring Your Crayons

Some surprisingly different variant sudoku constraints restrict the final grid to the same set of chromatic possibilities. Watch the reactions of YouTube sudoku streamers to these outcomes linked from our website: https://missingdeck.net/video-features, specifically the solves of Cross About Dominoes (by Cracking the Cryptic) and Restricted Skylines (by BremSter).

#### John Read: Bernoulli (Takakazu) Numbers

I gave a previous Mathsjam talk in 2013 about the Euler-Bernoulli engineering formula (talk title 1/384) which got me interested in other things that Euler and the Bernoulli’s (Jacob, Johan, Daniel) also worked on. This talk is about the Bernoulli numbers and some of their history. There are links between repeated integration, these numbers that arise in sums of powers, factorials, Pascal’s triangle, Fermat’s last theorem and the Reimann hypothesis that interested mathematicians over 300 years ago and have continued to intrigue ever since. These numbers were what Ada Lovelace was interested in when she wrote the first computer programme (her note D included an algorithm for computing the seventh Bernoulli number , although as printed it had an error in it).

#### Alyssa Burlton: Child's Play? The mathematics of stacking cups

When Sam came to stay with me one evening in September, we didn't have any plans. But then he mentioned something in passing: while watching his daughter playing with her stacking cups he'd thought, "there's probably some maths in this". Rum was poured. The whiteboard was deployed. This is some of what we found.

#### Tom Reddington: Tom's Dating Life

Applying a thin veneer of mathematical insight to get past the MathsJam censors, Tom puts his party trick to the test: you pick a notable (but dead) historical figure, tell Tom the birth and death years, and he will tell you who it was or greatly embarrass himself.

#### Jocelyn D'Arcy: Relationship status: 'real', 'imaginary' or 'it's complex'

A recent twitter problem set one quadratic expression raised to the power of a second quadratic expression equal to one. The solutions of where the base number was 1 or -1 or where the expondent was 0 were tweeted widely, but an error with a former suitor's code fooled me into thinking some complex solutions might exist. I think I ultimately proved that they do not, but am left wondering how the quadratics would need to change so that they could and if one complex number raised to the power of another can ever equal 1.

#### Ben Sparks: What are the chances?

A classic probability question with a surprisingly confident answer.

## SUNDAY

### SESSION 2a

#### Colin & team: Welcome back

Welcome to the day.

#### Andrew Taylor: A more intuitive model of the complex numbers

I was always taught complex numbers as "i is the square root of minus one" and from there it was simply asserted that raising e to a multiple of i lets you do trigonometry. That step always seemed quite opaque. But if you start by defining complex numbers via geometry, the identity of i as the square root of minus one is very easy to, well, if not prove exactly then at least make intuitive.

#### Clare Wallace: A Bodmas Sandwich

We've all seen the memes: "What's 6÷2(1+2)?" - and we've all tried to explain to someone that there isn't really a right answer: it's just a badly written question. I have a plan for how food can help us to put a stop to this nonsense, once and for all.

#### Toby Holland: How to not lose at games

A quick overview of rational behaviour, common knowledge, and iterated learning whilst playing games - using some data from previous MathsJam competitions...

#### Tarim: How do trains go round corners?

It's not as obvious as you might first think...

#### John Henry Hoskinson: Convincing a non-mathematician.

Conversations I had with a very clever friend, trying to convince him 1 = 0.9 reoccurring and how it lead to me coming up with a number of proofs to try convince him. Conclusion not always possible to convince a Non-maths using Maths proofs , There are many ways of proofing the same result.

#### Jen Sparks: RAF Maths

Some maths worth discussing that I see from a perspective of 10 years flying in the RAF and now being a secondary maths teacher.

### SESSION 2b

#### Goran Newsum: Sometimes it's OK to let your votes run-off

A short dive into the maths behind Run-Off electoral systems.

#### David Hartburn: Maths or Conspiracy?

Flat earth advocates dismiss the globe because the curve of the earth is "8 inches per mile squared". What does this actually mean and how does it compare to the real maths behind the curve of the earth?

#### Rob Woolley: Root of 1

How can you get from just 1 to everything we know about numbers?

#### TD Dang: The Fluid Dynamics of Incy Wincy Spider

TD discusses the mathematical equations describing fluid flow in a water spout. Would Incy Wincy spider (or its larger cousin, Chonky Donky spider) really be washed out?

#### James Grime: Birthday Magic Squares

James shows us how to make a birthday magic square.

### SESSION 2c

#### Katie Chicot: From MathsCity to MathsWorld

The UK is alone among the world’s industrialised nations in having no public attraction dedicated to the discovery and celebration of mathematics. From MoMath in New York City to Seocho Math Museum in Seoul, innovative maths discovery centres across the globe are engaging children and young people with maths, from an early age – inspiring interest and confidence in a subject that is at the cutting edge of research in global growth sectors such as engineering, medicine, Artificial Intelligence, FinTech and more. MATHSWORLD aims to transform the UK public’s perception of mathematics - revealing the engaging, aesthetic and surprising side of maths and empowering people to explore mathematics for themselves. In this talk I’ll show where the project is up to, what’s next and hopefully where you can get involved too.

#### Matthew Scroggs: Runge's phenomenon

I'll be talking about what can go wrong if you use polynomials to approximate things, and how you experiment with this using a Twitter/Mathstodon bot I made.

#### Adam Townsend: How tall is that bridge?

Adam wonders how many bridges he can drive a lorry under...

#### Gavan Fantom: The Laplace Transform

The Laplace Transform is widely used in certain fields of mathematics and engineering, and yet remains strangely unknown to the rest of us. Find out what it is and why it's so useful in this brief introduction.

#### Adam Atkinson: Maths for Time-Travellers, Briefing 17

Adam explains and demonstrates Prosthaphaeresis, a method for doing approximate multiplications that was used before logarithms were invented.

#### Annette Margolis: Extending the Twelve Days of Christmas to get the next Square Triangular number of Gifts

The total number of gifts on each day of the Twelve Days of Christmas is a triangular number, such that it is: 1 on the first day, 3 on the second, 6 on the third and so forth. However, on the first day and the eighth day the lucky (?) recipient receives 1 gift and 36 gifts in total respectively. How many days do we need to extend those twelve days so they receive another square triangular number of gifts? And is there a pattern to enable us to predict these square triangular numbers? Is there an infinite number of square triangular numbers?

### SESSION 2d

#### Competition results: Bakeoff

See the cakes page.

#### Competition results: Competition Competition

#### Robin Houston: Polyhedra whose faces meet at right-angles except on one edge

In 1968, the Swiss mathematician J-P Sydler described a hilariously complicated polyhedron whose faces meet at right-angles except on one edge where they meet at 45°. This suggests the game of trying to find other and/or simpler “single angle” polyhedra. Theoretically such polyhedra should exist for any angle whose sine (or cosine) is an algebraic number, but that theory doesn't tell you how to actually find the things. I'll explain what little I know about finding such polyhedra, and show some examples, and invite the audience to find more.

#### Hannah Gostling: I love hexagons!

Hexagons are awesome. I'll show you some reasons why.

#### Joel Haddley: Jim Morrison. Poet. Singer. Economist?

This talk seeks to contribute to the debate and analysis surrounding Jim Morrison’s lyrics.

#### Katie Steckles: The No-Three-In-Line problem

Katie explains the no-three-in-line problem, a simple geometrical puzzle which has an unexpectedly difficult solution - and remains an open problem.