# Maths Jam Conference 2015

Last weekend was the amazing mathsjam conference 2015. I’d like to start by saying a massive thanks to Colin Wright (@colinthemathmo) for organising it and another thanks to all the other people who helped organise, gave a talk, or just generally made it a fantastically fun event.

The post is mainly just to give a quick summary of some of the main things I enjoyed to take away and also to prompt me to write more full posts about some of them. If you couldn’t make it, I can summarise it by two days of maths fun featuring over 50 five minute talks (somewhat like a teach meet) and an evening full of further maths fun and puzzles. The main point of a 5 minute talk is to show something interesting, fun and/or cool about maths and then let people find you to ask about it in the (many) coffee breaks.

Anyway. Here are some things I liked. This is just notes in many cases and you’re welcome to ask more about anything that intrigues you. As I said, I’ll do further posts on a number of these items and it’s likely that if it looks unfinished below that’s because I plan to expand on it another time. Not all of the talks are listed. That’s not necessarily because I didn’t like them. It may be because I was too busy thinking about the previous one or because I didn’t understand it or just because it’s not something that grabbed me.

Finally, if you know what I’m talking about and are able to find suitable pictures, that’d be great!

Pedro Freitas : Maths Art – The Language of the Square by artist José de Almada Negreiros. (Need to find some pictures.)

Phil Harvey : Cumulative fairness. Split the numbers 1 to 16 into two groups such that:

- The sum of each group is equal
- The sum of the squares of each group is equal
- The sum of the cubes of each group is equal

There’s also a link to the idea of sharing things between A and B as a fair allocation. Linked to the Thue-Morse sequence.

David Singmaster : Iron grids over windows. There’s a type of iron grid over windows that looks as if it’d be impossible to put together. **Pictures? **There’s an impossible example of this sort of window in M. C. Esher’s Belvedere image.

Martin Whitworth : Coin tossing sequences. If you were tossing a coin lots of times, would you expect HTT or HTH to come up first? Penney’s game.

Pat Ashford mentioned Edmund Harris and Alex Bellos’ colouring book. Can’t tell you much but made a note to look it up. She had also made a wall hanging (about the same height as me) in the style of a QR code. Image here courtesy of Peter Rowlett

David Cushing : Magic and Gilbreath’s principle. This is to do with a very curious feature of a particular sort of riffle shuffle.

Kathryn Taylor : Hnefatafl. An ancient board game that is (very) vaguely similar to chess. Good fun and I beat Colin Beveridge at it.

Simon Bexford : 3D printing. Simon was showing a nice property of tetrahedrons and also demonstrating the work of his 3D printer. Find out more here.

Sam Headleand : DIY Calculating. Probably the talk of the event I would say. Sam wanted to make a Disco Calculator that would play tunes as you calculate. The existing one only plays one tune so, obviously, Sam breaks out her Raspberry pi and gets programming. This was a whole load of fun and epitomizes the idea of just having fun with coding and numbers. Anyway, I’m not going to do justice here but another post in in the pipeline.

Derek Couzens : Autological and Heterological words and a paradox. This was fun talk. I need to find out what words he used!

Rob Eastaway : Dabbling with Dobble. Has made me add Dobble to my christmas list.

Peter Rowlett : Nim-like games. Wythoff’s game on a chess board and plotting the ‘safe’ spaces. This needs more explanation but that’s for another time. Also the idea of an ‘exclusive or sum’ – wanted to find out what that meant and forgot to ask.

Adam Atkinson : asked for what values of a does a^a^a^a^a….make sense? An old question dating from 18 something.

John Read : Solomon’s hexagrams. John has baked biscuits of this puzzle. I ate one and it tasted of mathsy goodness. This is a puzzle game that looked lots of fun. He first heard of it from Super Games by Ivan Moscovich in 1984. Also see Peter’s comment below.

Elizabeth Williams : A ring with a fling to it. Carousels in America used to have dangling rings you had to try and reach for to get prizes. Elizabeth was mathematically modelling and asking about the possible maths behind them.

Yuen Ng : Diffie-Hellman Key Exchange. Using primes to send encrypted messages. g^ab = (g^a)^b = (g^b)^a (mod p). Again, more to come another time but helps explain why there’s money available for finding new primes.

Matthew Scroggs : How to set a chalkdust crossnumber. Partly an excuse to promote the excellent, new, free maths magazine I thoroughly recommend you go and check out their website and get hold of a copy. I particularly like the page 3 model.

That was the first day over!

I spent some time with Colin Beveridge and some others recording a special edition of Wrong, but Useful. Colin’s got a tonne of editing to do on that so it could be a while!

Also played several games and was reintroduced to the Tantrix puzzle game. Also on my Christmas list.

Day 2:

Ben Sparks : Conics and coordinates. A really nice talk showing how conic sections can be used to determine where planes are. Peter’s comment below offers this link.

Michael Borcherds : HAFF Ellipsograph no 97. Partly about a machine for drawing ellipses but also showing off Geogebra. Reminds me that I really must learn how to use geogebra. Link to slides.

Adam Townsend : The maths of chocolate fountains. A seductive title and showed why ketchup and blood should theoretically work in a fountain. Also showed a nice result involving blu tac, a 10p piece, a pencil and a tap.

Tiago Hirth : Six matchstick problems. I’ll show them sometime but you can imagine what this is.

Matt Parker : Magic Squares. There are many types of magic squares but there are some that haven’t been found yet. You could be famous by finding one of them. Here’s a website all about magic squares.

Colin Wright : Why Waves Wobble. What happens when you add two sine waves together? One of the nice points about this was Colin saying that sometimes a problem seems very simple but only when you’ve worked out the right place to stand and the right direction to look in.

Jonny Griffiths : Cambridge Maths Education Project. This a reminder that I should talk to Jonny about teaching maths.

Tony Mann : If I am telling the truth then I am the king. Nice talk and another one for the christmas list. The Magic Garden by George B by Raymond Smullyan is a book featuring logic puzzles.

Rogerio Martins : My bike is awesome. Was able to rip an arbitrary bit of paper, trace the outline with his bike’s tire and then tell us how much the paper weighed. No. Really. Apparently, this is called a planimeter.

Donald Bell : Interesting triangles. Talked briefly about what makes a good puzzle. I liked there points! Then introduced this one: Get five 3-4-5 triangles. Arrange them into a symmetrical pattern.

David Bedford : Balls in a Barrel Problem. Too complex to explain here but this was very entertaining and interesting to think about. Must ask him for more notes!

Simon Allen : Maths magic. Choose a 3 digit number. Repeat it. eg 264264. Divide by 7, then 11, then 13. He then went on to have a 9 digit number and repeated. He changed two numbers to make it divisible by 7! (that’s an exclamation point not a factorial.)

Josie Smith : Numbers are awesome. try these. 10/81 100/9801 100/9899 10100/970299 10000/970299

Colin Beveridge : Gaussian Machinations. The angles in three squares. (Need pic to make this make sense.) And an awful pun.

Joel Haddley : Reciprocal Prime Magic Squares. I was getting tired by this point but there was a clear “Oooh” moment from the crowd when he used the reciprocals of 7 to produce a magic square. See the links from Peter’s comments below.

Competition competition. I’m not going to do justice to this now but I liked a competition where you had to enter the number that you thought would be 2/3 of the mean of all the entries into the competition.

Phew. Sorry about the length of this post but I really wanted to enthuse about the weekend before I forgot too many details. There are a whole load of other talks that I liked too – please don’t be offended if yours isn’t above. Thanks again to Colin and everyone else. I’m off for a lie down.

EDIT: Thanks to Peter for some extensive additional notes below.

Thanks for the notes, which have filled a couple of gaps in mine. Here are some bits you might like more on, or answers to some of the questions you ask within the text.

Pedro Freitas: the subject was artist José de Almada Negreiros, who can be googled for pictures (possibly add ‘geometry’).

I have Phil Harvey’s talk as linked to the Thue–Morse sequence.

I don’t know the name to search for the window grills David Singmaster was speaking about, but there is an (impossible) example in M.C. Escher’s Belvedere.

The person between Martin Whitworth and David Cushing who mentioned Alex Bellos’ colouring book (actually Alex Bellos and Edmund Harriss’ colouring book) was Pat Ashforth. It was because she had a knitted panel inspired by a pattern in their book, photo here: https://twitter.com/peterrowlett/status/663004752377208832

I didn’t note down which words Derek Couzens used, but I did note that he said the paradox is (incorrectly) called Weyl’s Paradox but is by Grelling and Nelson (1908). My note says that essentially he asked: is ‘heterological’ autological or heterological?

I’ll leave you to google exclusive or sum. I guess email the speaker if you want to know more.

John Read may have mentioned Super Games, but his main focus was Games and Puzzles Magazine and I think this was where he first saw Eric Solomon’s hexagrams. See

http://boardgamegeek.com/wiki/page/Games_and_Puzzles_Magazine

http://www.davpar.eu/gamester/gamespuz.html

Yes, you have the end of the first day right – after Matthew Scroggs and before Ben Sparks.

The ideas in Ben Sparks’ talk were credited to this LMS/Gresham College lecture (which I was also at!), which you can watch online.

http://www.gresham.ac.uk/lectures-and-events/home-office-mathematics

I noted down the URL for Michael Borcherds’ slides (including GeoGebra demos) as: http://ggbtu.be/b1994635

Tony Mann’s title refers to Curry’s Paradox and credited the ideas in his talk to the books of Raymond Smullyan, including ‘The Magic Garden of George B. and Other Logic Puzzles’.

Rogério Martins made his bike into a planimeter.

I’m trying not to judge the missing ones as all experiences vary, but I’m surprised you haven’t included Ross Atkin’s talk about The Braess Paradox – his live cutting demo was one of the highlights for me.

Joel Haddley’s talk was nice. Do you have notes on what caused the ‘Oooh’ moment? It was basically this: https://oeis.org/A072359

More here: https://en.wikipedia.org/wiki/Prime_reciprocal_magic_square

Thanks very much Peter. This is quite a heroic addition!

I’ve added in some extra comments to the main body of the text and I expect I’ll be in touch about your talk.

As you say, I simply couldn’t take notes on everything and stay sane, but, care to jog my memory about Ross Atkin’s talk?

You’re welcome.

Ross spoke on the Braess Paradox. Basically that adding an extra road between two route options that took zero time/cost to travel on increased the journey time for both route options. His live demo involved a system of springs supporting a load such that cutting one made the supported load move upwards.

“exclusive or” is the logical operation A XOR B. It’s true when exactly one of A and B is true.

When calculating Nim sums you do bitwise XORs of the numbers invoved.

So e.g. 3 + 5 = 6 in Nim terms. (Both 3 and 5 have a 1 in the 1s place and those cancel. One contributes a 4 and one contributes a 2, so you get 6).

Thanks Adam. That helps a bit but I need to talk to Peter a bit more as I’ve pretty much forgotten the context of what a Nim sum is!

The “Nim Sum” of some numbers is the size of Nim pile you’d need to have for it to be equivalent to a collection of Nim piles with the sizes of those numbers.

so e.g. the Nim sum of 1, 2 and 3 is 0, which means if you see 1,2 and 3 anywhere in a Nim position you can ignore them.

And n+n=0 for any n so if you see two equal piles you can ignore them. (Unless they’ve already been ignored of course)

And the reason the Nim sum matters more than you might imagine is that lots of other games are basically Nim in disguise – https://en.wikipedia.org/wiki/Sprague%E2%80%93Grundy_theorem

I was the person who mentioned Alex Bellos’ colouring book. I used one of his designs as the basis of a knitted wall-hanging/blanket and am currently working on another version. (Although my talk was really musings about codes.)

Thanks Pat. I meant to mention your QR coded hanging. Will add that in!

Added a note in the body of the text now. Thanks again.

Incidentally the a^a^a^.. thing is very ancient (18 something) but I mentioned it in case there were people who hadn’t seen it. It can be done with A-level knowledge. (Disclaimer: not absolutely sure this is true in any particular current syllabus but there has been an A-level program at some point in time which included what you needed to do it.)

The Magic Garden of George B is a (relatively recent) book by Raymond Smullyan. He has done a fair number of logic puzzle books.

You’ve misspelt “Awesome” about my talk.

I’m afraid my spelling is spot on. :-p

Phil Harvey’s thing about 1-16 was generalised at a later mathsjam to be about 1..2^n and sums of powers up to 2^(n-1). Which I found fairly bogglesome at the time.

Great post Dave, thanks for sharing. Gutted to have missed it again!

Maybe next year…