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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

Dispute over mathematical music dismissed

By Peter Rowlett. Posted March 17, 2012

New Scientist reports on a lawsuit that was dismissed by a US district court this week, a decision apparently “intentionally released” on pi day. The case, “a claim of copyright infringement brought by one mathematical musician against another”, centred around a piece of music and YouTube video which went viral last pi day. Michael Blake, this says, created an “original musical composition, “What pi sounds like”, translating the constant’s first few dozen digits into musical notes”. The article explains:

That afternoon, jazz musician Lars Erickson from Omaha, Nebraska, cried foul. Erickson thought Blake’s work sounded suspiciously similar to his own 1992 piece “Pi Symphony,” also based on the digits of pi, which is registered with the US copyright office. He contacted YouTube, and Blake’s video vanished.

They had “both assigned each of the digits 0 to 9 to a musical note and then treated the digits of pi as a musical score”. Erickson calls the two melodies “identical”, but the court disagreed. The article reports the ruling:

the two pieces differed enough in areas like tempo, musical phrasing, and harmonies to be considered distinct. Plus, US law doesn’t protect every aspect of the piece, like underlying facts and ideas.

What’s more, Simon, who intentionally released his decision on Pi Day, noted that Erickson’s copyright registration only protects musical flourishes – and his are markedly different from Blake’s.

The legal opinion reads:

Pi is a non-copyrightable fact, and the transcription of pi to music is a non-copyrightable idea. The resulting pattern of notes is an expression that merges with the non-copyrightable idea of putting pi to music.

Read the full story at New Scientist: US judge rules that you can’t copyright pi.