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Double Maths First Thing: Issue 21

By Colin Beveridge. Posted April 23, 2025

No dragons were harmed in the making of Double Maths First Thing.

Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight in numerical noodling, patterny playfulness and generally messing about with maths.

This week I’m back at my desk after a long Easter break. There are stories to write, bugs to catch and some travelling to do. On with the show!

Links

Let’s start this week with Dominika Vasilkova’s inspirational article about cardioids in coffee cups, which deserves more credit. Geometry and coffee, what’s not to like?

Something I very much don’t like (yet) is multiplying 0.333… by 0.444… without using fractions to get 0.148148…. I find it deeply disturbing. Richard Plagge explains how it works, and I would certainly not recommend using a site like Sci-Hub or note that the paper’s DOI reference was 10.2307/3026549. That would be irresponsible and probably lead to the collapse of the whole publishing industry.

Something that does use fractions is Conway’s ridiculous programming language, Fractran. Reginald Braithwaite has a nice write-up of it.

Another thing that uses fractions, but incorrectly, is Iceland’s parliamentary voting system, which assigns top-up seats per region based on the national vote. That’s a Good System in my book — unfortunately, they use the wrong formula. Unlike Geneva, which rocks.

One more troublesome fraction thing? Oh, go on then. Here’s Lior Sinai’s story of how it took almost 100 years to integrate sec(x), and how it was discovered experimentally.

Currently

There’s a Finite Group livestream next week — you should definitely join up and send them money. If you did, you’d be able to watch Scroggs and Katie talk about squares. Who better?

I can also remind you that the Pseudorandom Ensemble will be headlining — or at least going on last — at the Clopen Mic night on Thursday May 1st. The show starts at 8pm, and it’s pay-what-you-like.

That’s all I’ve got for this week. 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.

Meanwhile, 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 you want to tell me.

Until next time,

C

Double Maths First Thing: Issue 20

By Colin Beveridge. Posted April 16, 2025

Double Maths First Thing doesn’t look an issue older than 1F

Hello! My name is Colin and I am a mathematician on a mission to spread joy in the creativity and beauty of maths, in the delight of figuring things out and asking more questions. This week, I’ve been playing with continued fractions, and finally have a better sense of how to compute them for a given square root. There may be a blog post ahead.

I’m finally able to confirm that the Pseudorandom Ensemble (one of the UK’s top ten mathematically-inspired musical combos, and of which I form a fraction) will be performing at the Clopen mic night on May 1st from 8pm, doing something perfectly normal. It’s free, although donations are encouraged.

Links

Some weeks I struggle to find any good links, but this week — possibly because I’m on Easter break and checking mathstodon more frequently than usual — I’ve almost got too many.

Let’s start in Ukraine, where there’s been precious little good news recently: however, President (and voice of Paddington) Volodymyr Zelenskyy has recently opened the Cuboid Museum of Mathematics in (if my Cyrillic deciphering is correct) Kyiv. I hope to visit it in a peaceful future.

Back in issue 17, I mentioned a variation on the Elo method used in chess rankings — I love such things. Elo is great, but limited by its assumptions; I’ve recently seen two more variations that try to get around this: Microsoft’s TrueSkill2 and Mark Glickman’s Glicko. If only there were some way to figure out which was better.

While we’re on the subject of uncertainty, Filip Hráček has a lovely calculator for use with inexact data. It’s adequate~amazing.

In the world of mathematical crafting, Anisa du Plessis has a fantastic article about the maths of crochet, which is worth skimming for the pictures alone.

Currently

At the Aperiodical, Elinor has reviewed some of the art inspired by Ayliean’s Math Art March prompts — again, plenty of gorgeous visuals here.

Tuesday coming is the traditional day for the April MathsJam — as usual, I’ll be at the Weymouth version, and you can find your local one — or find out how to start your own — here.

That’s all I’ve got for this week. 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.

Meanwhile, 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 you want to tell me.

Until next time,

C

Double Maths First Thing: Issue 1F

By Colin Beveridge. Posted April 9, 2025

Double Maths First Thing only exports lost puffins

Hello! My name is Colin and I am a mathematician on a mission to spread joy and delight, and to find excuses to do interesting maths. (If you could use an interesting mathematician — for the purpose of solving problems, slinging code, writing content or making the world a better place, give me a shout!)

This week it’s the first half of the Easter break here — and the kids have finally reached an age where they value a lie-in. I finally understand why middle-aged people say the morning is the best part of the day: you can get on with stuff without having to referee squabbles of tell them to turn Spongebob down for the fifteenth time.

Links

Let’s start with some lovely mathematical art: Dori the Giant’s 13 Animals, each made from 13 circles. I think the walrus is my favourite.

I enjoyed this tootstorm from Robin Houston about Yuu Asaka’s deconstructed jigsaw puzzles. I love it when someone says “it’s always this way. Why not do it a different way?”

Unless, of course, they’re in charge of the world’s largest economy and don’t have a Scooby-Doo what they’re doing. Matt Parker has the breakdown, so that I don’t have to.

While doing research on mountweazels, I came across the Wikipedia page for Claude Litre. Having written a song that claimed there was an SI unit named after Nelson Candela, I heartily approve.

I suppose there ought to be something halfway serious in here, even if it’s the holidays: here’s a nice piece about breaking down tricky probabilities.

Currently

We’ve got a new Carnival of Mathematics courtesy of Fractal Kitty — in case this round-up of interesting maths isn’t enough for you. (It includes many things I missed).

One of the perks of running a newsletter is that I get to promote excellent work by excellent people — if you teach maths, and need either 15-minute activities (which can be stacked to make longer sessions), you should check out Alison Kiddle and Katie Steckles‘ webshop at 15minutemaths.com

That’s all I’ve got for this week. 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.

Meanwhile, 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 you want to tell me.

Until next time,

C

Double Maths First Thing: Issue 1E

By Colin Beveridge. Posted April 2, 2025

Double Maths First Thing picked the wrong week to give up calculus.

Hello! My name is Colin and I am a mathematician on a mission to spread the joy and delight of doing mathematical things.

It’s nice to finally be in a new month after April 1st was cancelled again, the 32-day March always catches me out. Rather than the tedious April Fools’ jokes, some people instead do April Cools, where the only surprise is that the author is writing on an unexpected topic. Here’s the manifesto. I approve.

Links

One of the things that goes on in April is Easter — it’s fairly late this year. In case you’ve ever wondered how to calculate it, Verge Cornelius has a guide. Bring back decimal time, I say.

My eldest has recently been playing a lot of chess. This reminded me of the Chess Mysteries of Professor Smullyan, a book of which I remember reading close to four decades ago. “Retrograde analysis” involves not finding the next move, but determining the last one. There’s a lot of maths in that.

In retrogaming news, Ben Shoof has got to the bottom of The Colonel’s Bequest, an endearingly ridiculous deep-dive into completing an ancient computer game.

From the art world, here’s a look at Piranesi’s perspective trick; Bruno Postle investigates how Piranesi drew realistic-looking panoramas by slightly bending reality.

Robert Abbott is a legend in recreational maths — I remember playing Theseus and the Minotaur far more than I should have done back in the day, and Eleusis is a fantastic invention. I was recently pointed at his logic mazes, which look equally entertaining.

Currently

I’m hearing rumbles about a Clopen Mic Night next month — I’m not at liberty to say any more, but I expect it to be a cracker.

March’s TMIP animation challenge is over — check out the videos here — but never worry, another edition has already begun and you can submit your polyhedral nets over the next month.

Also, if you’re so minded, you can take part in What’s My Plot?, an occasional series in which I post an unlabelled plot and you guess what it is.

That’s all I’ve got for this week. 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.

Meanwhile, 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 you want to tell me.

Until next time,

C

Double Maths First Thing: Issue 1D

By Colin Beveridge. Posted March 26, 2025

Double Maths First Thing just doesn’t know any more

Hello! My name is Colin and I am a mathematician on a mission to spread delight and joy in doing maths for the sake of it.

This week I have mainly been figuring out the mechanics of the Bokeh library so I can make it draw graphs. It’s really neat! (Now drawing graphs is a service I offer at a reasonable consulting rate.)

I’ve also been making progress with blindfold cubing — I managed a successful solve on the bluetooth cube in under 5:30, which is slower than I’d like; however, there’s plenty of time until the competition to get quicker and more reliable. (Talking of cubing, there’s a wealth of data available here.)

Links

Frank Lantz loves SET in a different way to how I do. If you don’t own it, you can get it from MathsGear for a tenner or so (UK).

Here’s an interesting (but ultimately, unsatisfying) article from Quanta via Wired about a new kind of hash table. I think my problem with this kind of article is that I want to know a bit more about the detail and a bit less about how it made people go wow.

Much more in-depth: this one’s about different sorts of means.

Finally, a curiosity: a number’s Zeckendorf decomposition is the unique way it can be written as non-consecutive Fibonacci numbers, so (e.g.) 20 = 13 + 5 + 2. You can use the Zeckendorf decomposition to factorise numbers, although it turns out to be pretty slow.

A geeky aside

I found out this week that Paul Erdős appeared as himself in the documentary N is a Number, as did Tomas Luczak.

Luczak had a minor role in The Mill and the Cross, which also featured Charlotte Rampling.

Rampling and Martin Sheen both had acting credits for Jerusalemki sindrom.

And Martin Sheen was in JFK with Kevin Bacon.

Therefore Paul Erdős has a Bacon number of four — and also an Erdős-Bacon number of four. (Nicholas Metropolis, according to the Wiki, is also a 4.)

My Erdős number is 5+i; the i was bestowed upon me at G4G after I wore Erdős’s coat.

As it happens, today is Erdős’s 112th birthday. Here’s Katie celebrating it a few years ago.

Currently

There is a partial solar eclipse on Saturday coming (March 29th), visible across most of Europe and around the North Atlantic. Don’t look directly at the sun, unless of course you’re the President, in which case feel free to ignore that woke nanny-state nonsense.

Registration is open for the Zeeman Award ceremony on May 7th in London — you don’t get a Zeeman Award without being a legend; this year’s laureate is Brady Haran of Numberphile. (The dates are all over the place on that page, but I’m assured it’s this May.)

And I deliberately missed off Chris Smith’s maths newsletter from “here are good places to get maths content” last week — but only because I needed to check with him about how to sign up. You email aap03102@gmail.com and he’ll be delighted to have you on board.

That’s all I’ve got for this week. 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.

Meanwhile, 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 you want to tell me.

Until next time,

C

Double Maths First Thing, Issue 1C

By Colin Beveridge. Posted March 19, 2025

Double Maths First Thing cannot currently take your call. Please leave a message after the beep. Beep.

Hello! My name is Colin and I am a mathematician on a mission to spread mathematical joy and delight. This week, I am mainly swearing at Scroggs and his fiendish crossnumber in the current issue of Chalkdust Magazine. He’s also written an article about how to set the cursed things, but it offers no clues (at least to me) about solving them.

But fine, I shall tear myself from tearing out what little hair I have remaining to share with you this week’s links.

Links!

Let’s start with the best title of the week: The Mathematics of Burger Flipping. I am a big fan of papers that take a reasonable question to unreasonable extremes.

Another reasonable question is, “how does GPS work?”. Ankur Mohan has a deeper dive than you could plausibly need.

A less reasonable question is, “can I link all 72 scientists named on the Eiffel Tower to pi?”. However unreasonable, since it was Pi Day, Katie Steckles had a creditable attempt, no matter how tenuous some of the suggestions are. Can you find a connection between Jacques Sturm and circles? Let her know if so.

(Incidentally — if you have reasonable questions that need a freelance mathematician to answer or explain, you can hire me at a rate which is also — you’ve guessed it — perfectly reasonable.)

I mentioned Perlin noise all the way back in issue 2; James Wilkins has a tutorial on how to use it to generate anything from landscapes to dungeons. This is on my still-to-read list, but looks awesome.

And let’s finish with a lovely bit of dataviz from Information is Beautiful, answering another reasonable question: how true are “based on a true story” films?

Currently!

I didn’t mention in last week’s issue that I had a poem in the MathsJam Shout. I don’t remember writing it, but it’s the sort of thing I would do. It was a Pi-ku (a poem of three lines, the first having three syllables, the second one and the third four — 3-1-4, sort of like pi.) It read:

Rational?
Pi?
Mumbo-jumbo!

I don’t have any upcoming events on my radar (if there’s something you’d like me to mention, do let me know). As always, you should be hanging out in the Finite Group Discord, keeping an eye on Talking Maths In Public, and telling anyone who will listen about the maths you find interesting. Go to!

That’s all I’ve got for this week. 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.

Meanwhile, 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 you want to tell me.

Until next time,

C

Double Maths First Thing: Issue 1B

By Colin Beveridge. Posted March 12, 2025

Double Maths First Thing thinks ISO8601’s great

Hello! My name is Colin and I am a mathematician on a mission to spread mathematical joy — I almost misspelt “mathematical” as “mayhem”, so let’s have a bit of that, too.

I spent much of the weekend with a secret cabal of mathematical musicians at an undisclosed location. I’m not authorised to say whether we were rehearsing original maths songs and I certainly couldn’t comment on rumours of a future gig on the roof of the RI. By which I mean, you’ll likely hear more details in the future.

Links

What’s been on my radar this week? Well, r/math has been surprisingly interesting, with a dissection of a square into 32 similar triangles and a nice pandigital approximation for e.

It was pointed out to me that I didn’t say what I was trying to solve blindfold last week. To clarify, I’ve been learning the M2 method for solving the Rubik’s Cube. If you were a computer, you might prefer a more brute force method.

When I was about 8, I got into trouble at school for saying “DAMN!” when my Polydron dodecahedron collapsed. If you want to have the same experience of frustration, you can get a 10% discount over the next few months. (That’s not an affiliate link, we don’t roll that way around here.)

A way we do roll is to stand up and say “oi! no!” to bullies. I’m conscious that I have pretty close to a full bingo card of privilege, and that a lot of the toxic behaviour in academia flies beyond my radar. Dr Rachel Los’s Anti-Acknowledgements (p113), (or more conveniently, in a toot) in her thesis (brilliantly titled “Play Nice or Pay the Price”) make me sigh in despair; men need to stop behaving like this, and the “not all men” men need to call out this sort of behaviour.

Currently

Less upsettingly, there’s a lot going on at the moment! This week has Pi Day, about which I am largely curmudgeonly, but some people erroneously believe it’s more Geek Christmas than Big MathsJam is. Whatever, you do you!

Tuesday coming (March 18th, 2025) is the traditional time for your local MathsJam — find your nearest one here, along with instructions on how to start your own if the nearest one is inconvenient. There’s also an online (UK) one if that’s better for you.

And on Monday coming (March 17th), there’s a Finite Group livestream. The FG Discord is a great hangout for mathematicians, and I always enjoy watching the livestreams with my 11yo.

Last week, I neglected to mention that TMiP is organising an Animation Generation Collaboration — a challenge to see what people come up with, and to share techniques.

That’s all I’ve got for this week. 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.

Meanwhile, 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 you want to tell me.

Until next time,

C