Is the Carnival of Mathematics back in town already? It feels like it’s hardly been six months since the last one.

This is the 242nd Carnival, and – as is traditional – I need to give you some facts about the number. My first observations were that it’s $2 \times 11^2$ and $3^5 -1$. That second form means it’s automatically $(3-1)\left(3^4 + 3^3 + 3^2 + 3^1\right)$, but as far as I know it’s a coincidence that those powers sum to 121.

Number Gossip tells me it’s also the smallest integer $n$ such that $n$, $n+1$, $n+2$ and $n+3$ all have the same number of divisors (6), and that $2^{242}$ is the smallest power of two to contain the string “000”. It’s palindromic in base 10, but also in base 3, where it is $22222$, and base 7, where it is $464$.

David Benjamin points out that $242^{242}$ has a prime number of digits, namely 577. Meanwhile, $117^{117}$ has 242 digits, as does $¡140!$. (Around here, we do Spanish-style factorials.)

Serious things

In Tom Robbin’s Even Cowgirls Get The Blues, there’s a running motif of news of the international situation being “desperate, as usual”. Particularly in the US, it seems that maths and science funding is in a more parlous state than usual.

If you’re not from an academic background, you may be unfamiliar with the process by which scientific papers are published. I certainly was when I started in academia. I thought you wrote your paper, sent it in, the editors fixed your spelling and, I dunno, graded it with a truth-o-meter and printed it. Turns out that isn’t the case: what happens is, the editors decide whether it’s interesting. If so, they send it to two or three experts in the field, who (in principle) go through it with a fine-toothed comb to make sure it makes sense, and a game of editorial ping-pong ensues. Eventually, hopefully, something correct gets printed. Computational Complexity has a report of a case where this, apparently, didn’t happen properly.

Peter Cameron uses the occasion of his retirement to talk about his academic family((Corrected 2025-09-02 to finish the sentence)) – congratulations, Peter.

I don’t know how many Carnival-goers ever need to compute generalised hypergeometric((Corrected 2025-09-02 – I originally said “hyperbolic” because I wasn’t paying attention)) functions from series – they look like the sort of thing that shows up on Wolfram|Alpha when the answer is too hard for mortals – but in case you’re one of them, Skewray Research has a series of posts that might help.

In inspiring news, Ioanna Georgiou invites us to join the conversation on using stories to bring maths to life. I’m just back from the Talking Maths in Public conference – which was as excellent and exhausting as it always is – where there were several discussions about humanising maths with stories.

Recent news

All of the buzz in the last week or so has been about the noperthedron, the first convex polyhedron that’s been proved that’s been proved non-Rupert. Perhaps, like me last week, you wouldn’t know a Rupert polyhedron from Rupert the Bear: John Carlos Baez explains (with pictures) that you can fit a cube through a hole in an identical cube – that’s Prince Rupert’s property, that you can (in principle) drill a hole in the shape and pass a copy of the shape through the hole. It is conjectured that the rhombicosidodecahedron is non-Rupert, but I understand that proving such a thing is not the easiest task.

(I learned from Ayliean this week that the octahedron is the only Platonic solid you can make with a single modelling balloon, which is an excellent maths fact, the sort that takes a moment of thought but then becomes obvious.)

Terry Tao, like balloons (and Ayliean), is super-cool. He and Ayla Gafni have a paper on rough numbers between consecutive primes; he’s also been involved in solving another open problem of Erdős. He’s also also crowdsourcing an effort to link erdosproblems.com to the OEIS. I note that he’s been described as a “friendly fire-hose of math[s]”, which I think is an excellent career goal for everyone, and which I’ve adopted as my LinkedIn tagline (please hire me for cool maths projects!).

Cool and interesting things

Perhaps you’re one of today’s lucky 10,000 who didn’t know that Lewis Carroll (or rather, his alter ego Charles Dodgson) was a mathematician. There’s a school of thought that sees Alice in Wonderland as a satire of the ‘new’ mathematics of the Victorian era. John D Cook notes that several zero knowledge use elliptic curves named after characters in Through The Looking Glass.

We’ve got several posts from John this month. The next is a visual intuition for Pick’s theorem, which states that the area of a simple (non-crossing) polygon whose vertices lie on a grid is equal to the number of points inside it plus half the number of points on the edge. John’s post shows clearly why it works for rectangles, although the more general case appears to be left as an exercise.

Like John, I dislike misleading graphs. I had to have a little cry at the otherwise excellent Coventry Transport Museum. However, John’s little cry this month is about how elliptic curves are presented (and how they should be).

Robin Whitty at Theorem of the Day credits another of John’s posts in his comments on Moessner’s magic (and apologises for not submitting it to Carnival 241).

Something I’m rather too tired and frazzled to put effort into understanding right now is this lovely-sounding construction from David Eppstein: a smooth (continuously differentiable) curve with no convex arcs.

If you were one of the lucky people at the Pseudorandom Ensemble show at the Warwick Arts Centre last week, you’ll know that the Rubik cube is a SCAM perpetrated by Big Geometry to sell more polyhedra. Bryan Wolf has figured out exactly how scrambled a cube can get.

Polyhedra, you say? Here’s a short video from EduAbility showing the Euler characteristic. In Excel, which is certainly a choice.

Also in the “important applications of maths to real life” folder, The Pudding investigate and illustrate the best way to chop an onion.

When I was at school, entertaining maths books were limited to Martin Gardner and Ian Stewart (who I was thrilled to meet and gush at last week). (Possibly Raymond Smullyan). Then along came a new kid on the block, Rob Eastaway, who has recently rearranged his posts into more useful topics and highlighted several of his most notable articles, from which I pick this one about tennis serves as a personal favourite.

Also also, my dear friend Tom “Thomas K Briggs” Briggs has a post about the maths he found on a visit to Bolsover Castle. Incidentally, he has a new book out, The Mathematician’s Library. I’ve read it, it’s good.

A plug!

If you’re in the market for a weekly maths “here’s a cool thing” digest that arrives in your inbox on a Wednesday morning (UK time), you should sign up for Double Maths First Thing, which celebrates its first anniversary this week! You can also read it ‘syndicated’ (yes, seriously, I have heard myself) at the Aperiodical.

Thanks to…

Everyone who’s submitted articles for this Carnival, including John D Cook, Rob Eastaway, Sophia (FractalKitty), Christian Lawson-Perfect, Skewray, Katie Steckles and Robin Whitty

If you’d like to volunteer to host a Carnival, or look at previous Carnivals, you can do so at the Carnival page at the Aperiodical. Without people to host the posts, the show can’t go on. The next event will be hosted by Ioanna Georgiou and available in early October.

* Edited 2025-09-02 to fix various spelling and linking errors.