The Aperiodical 

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Double Maths First Thing: Issue 9

By Colin Beveridge. Posted November 6, 2024

Double Maths First Thing is like a diet MathsJam, some of the flavour but only a hint of the joy.

Hello! My name is Colin and I am a mathematician on a mission to spread delight in my beloved subject.

I spent the weekend at Big MathsJam in Staffordshire and gorged myself full of puzzles, surprises and fascination — my personal highlights were Mats Vermeeren’s talk about why the start lines on athletics tracks are curved the way they are, Vincent van Pelt’s MathsJam Jam song (Mnemonic to the tune of Blondie’s Atomic) and the colouring-in in the quiet room. Now I’m sad that I don’t get to do it for another year.

From around the internet

It’s always cool to see ancient technology in action. Slide rules may not be ancient ancient, but they were no longer in common use by the time I was at school. (I remember we had some Napier’s bones, but nobody knew how to use them. I wish they had, I’d have lapped it up.)

As everyone knows, the Mathematical Villain goes through your spreadsheets turning data into dates. Here are some more times that Excel users failed to, well, excel. (Aside: it’s all so avoidable! A halfway-competent programmer can set up a script that checks for this sort of thing. And if you need one of those, you should let me know.)

In “everything is interesting if you look at it closely enough” news, the horrors of implementing daylight saving rules around the world are fascinating.

I also loved this bit of code golf for finding Fibonacci numbers. The explanation is much more interesting than the code.

I couldn’t explain why, but I’m averse to calculator notebooks. Not my cup of tea. Don’t like Jupyter. I may have had a bad experience with Maple as a student. That doesn’t mean you can’t experiment and enjoy, though!

Lastly, to file under “ridiculous but brilliant projects”, several generators of the Finite Group are challenging humankind to say the new record Mersenne Prime before the next one is discovered. Join the race!

Books!

Apparently some people celebrate Actual Christmas rather than (or as well as!) MathsJam. That’s OK, all are welcome. If you’re looking for maths-related books to buy someone so they can add them to the unread pile on the floor, here is a selection of books I’ve either read and enjoyed or have had recommended to me:

• Alex Bellos’s Think Twice
• Rob Eastaway’s Much Ado About Numbers
• Pippa Goldschmidt’s Schrödinger’s Wife
• Matt Parker’s Love Triangle
• Ernő Rubik’s Cubed
• Olivia Waite’s The Lady’s Guide To Celestial Mechanics

(Note: these links don’t necessarily go to the cheapest place to order from. I recommend asking your local independent bookshop — if you don’t have one of those, Gulliver’s in Wimborne deliver across the UK and are lovely people too.)

In the meantime, if you have friends and/or colleagues who would enjoy Double Maths First Thing, do send them the link to sign up — they’ll be very welcome here.

If you’ve missed the previous issues of DMFT or — somehow — this one, you can find the archive courtesy of my dear friends at the Aperiodical.

That’s all for this week! If there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website. You can also just reply to this email if there’s something I should be aware of.

Until next time,

C

Double Maths First Thing: Issue 1

By Colin Beveridge. Posted September 11, 2024

Double Maths First Thing is Colin’s weekly news summary. Or autumnal, if you’re reading this after the equinox. You can sign up to receive it in your inbox on a Wednesday morning here.

Hello! My name is Colin and I am a mathematician. It’s Wednesday morning, and it’s Double Maths First Thing.

Shape-ology

Over on the Talking Maths In Public WhatsApp group, we’ve been looking at collapsible polyhedra, which Barney Maunder-Taylor calls Flatonic Solids. He’s not the only one, though: here’s a satisfying Instagram reel and an article by Liz Meenan in case you want to make your own.

It also reminded me that you can do cool things with pop-ups, whether or not you have the book.

Speaking of books

Tom Briggs has been compiling suggestions of maths books that aren’t about teaching. I’m given to believe he might be making his own addition to the list in due course.

Peter Rowlett and his son have been reading Gulliver’s Travels, and found an interesting early description of something computery. A biased generator of randomness that produces plausible English? I bet the venture capitalists would be all over that.

Sudoku

I recently had cause to revisit the Miracle Sudoku video — memorably described at the time by Ben Orlin:

You’re about to spend the next 25 minutes watching a guy solve a sudoku.
Not only that, but it’s going to be the highlight of your day.

The highlight of my day recently was coming across Phistomephel’s ring, which is a neat consequence of standard sudoku rules.

Tony Mann pointed me at another Cracking the Cryptic video with the same energy — the frustrations and feelings of stupidity that come with not having the answer yet, followed by the sheer joy of having worked out something clever.

Another (and significantly shorter) video plausibly worth your time is Alyssa Williams and Christian Scott at G4G discussing how to set variant sudoku.

Joy in maths

Back to taking pleasure in maths, here’s a short interview with Talithia Williams, PhD: I loved the bit about maths appreciation, and trying to change the mindset that maths is about doing calculations to pass a test.

Another article that caught my eye this week was about climbing. Or rather, spotting an error on the climbing wall and getting it fixed. It’s interesting for several reasons, but what grabbed my attention was what I think of as x-ray vision: the power to see that something looks off, and the insistence that it be put right. That strikes me as a very mathematical thing. (And, speaking for myself, possibly an autistic thing. Drives me MAD when people don’t care about breaking the rules, I tell you.)

For your listening pleasure

This week, I have mostly been listening to:

• Tim Harford’s Cautionary Tales
• Bec Hill and Matt Parker’s A Problem Squared
• Evelyn J Lamb and Kevin Knudson’s My Favorite Theorem
• Katie Steckles and Peter Rowlett’s Mathematical Objects — I understand that series 8 is imminent.

I’ve not yet picked up the TMiP podcast, but we all should. And Sam Hansen would give me endless, deserved grief if I didn’t mention Relatively Prime.

The week ahead

Thanks to September ending on a Monday, the monthly MathsJam meet-up is coming around distressingly quickly — those that meet on the traditional penultimate Tuesday will do so on September 17th. You can find your local MathsJam here — I’ll be at the Weymouth one.

Also, if you’re planning to go to Big MathsJam in November, early-bird pricing ends on Sunday.

There’s a Finite Group livestream on Friday, September 13th at 9pm BST — Katie and Ayliean are putting the ‘fun’ into ‘fundamental theorems’, it says here.

That’s all for this week! If there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website.

Until next time,

C

Double Maths First Thing: Issue 0

By Colin Beveridge. Posted September 4, 2024

Double Maths First Thing is Colin’s weekly news round-up. Or round-down, if the fractional part is smaller than a half. You can sign up to receive it in your inbox on a Wednesday morning here.

Hello! My name is Colin and I am a mathematician. Welcome to issue 0 of Double Maths First Thing, in which I highlight some of the mathematical things that have caught my eye this week.

Let’s talk about \( \pi \) and powers

First up, a nod to physicists Arnab Priya Saha and Aninda Sinha for doing something with no real application: they “accidentally discovered a new formula for pi”. There’s a bit about it in Scientific American, a Numberphile video, and a paper in Physical Review Letters (open access). I’ve not worked through it in detail, but it’s got a Pochhammer symbol in it, so it must be good.

I promise this isn’t always going to be about pi, but I also stumbled on a proof that pi is irrational — again, I’ve not worked through the details, but it looks like it would be accessible to a good A-level class with a bit of hand-holding.

Via reddit, a surprisingly tricky problem with a lovely twist in the tail: show that \( 3^k + 5^k = n^3 \) has no solutions for \( k > 1 \). (There’s a hint and a spoiler over on mathstodon.)

Somewhere to visit: W5, Belfast

I’ve recently been on holiday in Northern Ireland. We visited W5 in Belfast, which is a pretty cool science museum — lots of hands-on stuff, including a build-your-own Scalextric-style car, bottle rockets and a green-screen bit where you can present the news about the alien invasion. On the minus side… there are lots of missed opportunities for highlighting the maths that underpins it all. Still, it’s a fun half-day if you’re all Titanic-ed out. 

Maths in the news

In the proper news, the Guardian had a long read about Field’s Medallist Alexander Grothendieck; although it too is a bit maths-light, it’s understandable given quite how heavy Grothendieck’s maths is. Katie Steckles also pointed me at the devastating news that UK railcard discounts are dropping from 34% to 33.4%, which strikes me as the sort of thing that probably costs more to implement than it could possibly save the train operators.

Upcoming maths

If you’re in the market for more maths, I can heartily recommend both the Finite Group, whose next livestream is on Friday September 13th, and Big MathsJam, which is a gathering of amazing geeks the first weekend of November. Early-bird tickets are (just about) still available; I have mine already. There’s also a day of recreational maths lectures in memory of David Singmaster on Saturday September 21st in London or online, and a New Scientist event about how maths explains the world the following Saturday, also in London.

That’s all for this week! If there’s something I should know about, you can find me on Mathstodon as @icecolbeveridge, or at my personal website.

Until next time,

C

The Double Back puzzle is a nice mix of Towers of Hanoi and Solitaire

By Christian Lawson-Perfect. Posted December 10, 2023

This post is both a video and text. The content is largely the same in both versions, so you can pick one to look at.

I’d like to show you a puzzle, or game for one person, that Ed Kirkby came up with. Ed showed this to me at the Big MathsJam gathering last year.

I was walking around MathsJam and people were doing all sorts of stuff and Ed was quietly sat at a table with some cards in front of them, and a couple of people were gathered around with thoughtful faces, so I thought “oh that looks interesting” and I walked over and Ed explained the rules of this game to me.

And like most things at MathsJam, I didn’t immediately know the solution but it really got to me, so I went away and tried to find a solution myself. It was really fun and it was one of those pure experiences of mathematical discovery that you really remember.

I kept grabbing other people and saying, “have you seen Ed’s puzzle? Come over here. Ed, explain this puzzle to this person!” I did that for the duration of the weekend, and for a little while after I got back home.

I’ll show you what the puzzle is.

Take two sets of cards numbered 1 to 4, and lay them out in two rows. The game is to get them the other way round, so each row goes 4, 3, 2, 1.



The things you are allowed to do are to swap two cards that are adjacent numbers and in adjacent columns.

So you can swap the four and three here:

You can also swap to the other row.

You can’t swap the four and the two here because they’re not adjacent numbers.

It’s a permutations puzzle. And with a bit of thinking, a lot of just making random moves, eventually I worked out how to do it for four cards (or two lots of four cards, to be precise).

It took me a few more goes to be sure that I’d found the shortest solution — the fewest moves — but then five really stumped me.

When I tried six cards, I wasn’t sure it was possible at all: there was a point where I kept getting stuck.

So I was really unsure, and Ed was unsure as well – they didn’t know if there was a solution for every number of cards. They’d written some code that very slowly churned out solutions for small $n$, but didn’t have a general solution.

So I did my usual problem solving technique which was, if I couldn’t do it with four cards, do it with three cards, and very briefly with two cards. Then after a while I sort of started seeing a pattern.

I came away from Big MathsJam not knowing how to solve this puzzle.

I kept playing with it when I should have been working, and eventually I think I’ve sort of got the vibe of how it works and I’m pretty sure now I can solve it for any number of cards. I haven’t written down a really rigorous algorithm for doing it but I’ve got a general idea.

Interactive version

Something that often happened when I was playing with cards was that I’d forget which way I was going, because when you don’t have a strategy you’re sort of making lots of moves to see where they’ll go, and then maybe you want to backtrack a bit, and you go like wait wait — which end did the aces start at? You’re continually picking up cards and moving them, and if you’re as clumsy as I am they scatter all over the place and you end up unsure if you’re in a valid state.

So it won’t surprise you to learn that I made an online version of this.

Big MathsJam happens in November, and by the time I’d got this online version working it was getting close to Christmas and I thought, “we need something that’s not playing cards to be the pieces – why shouldn’t it be baubles? They’re circles, they’re easy to draw.”

So I spent some time drawing a bauble image and making it look Christmassy. I didn’t quite get it ready for last Christmas, so I spent some more time improving the interface and I made it fully keyboard accessible.

And then I made a note to write a post about it in December 2023. And here we are!

I think this is a nice Christmas puzzle: I think the set-up and the rules are easy to remember, and it only needs a pack of cards, which you’ll probably have lying around.

So over Christmas, if there’s a quiet moment, if you get some playing cards in your Christmas cracker or just some pieces that you can put in an easy to identify order, try showing this to someone.

So there you go, that’s the Double Back puzzle, invented by Ed Kirkby, online version made by me.

The Maths Podcast to end all Maths Podcasts

By Katie Steckles. Posted December 2, 2018

At the MathsJam weekend gathering earlier this month, we found ourselves invited to join maths podcasting supremo Samuel Hansen for a recording session. Nothing unusual there: podcasts have been recorded at MathsJam before. But this time Samuel wanted to record more than one podcast at the same time – since many of the maths podcasting community were present, it seemed like a good plan to grab anyone who wasn’t already doing something else and record something quite unlike any podcast you’ve ever heard.