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How to fold and cut a Christmas star

This week and last I hosted a series of public maths talks featuring disabled presenters. I’ll post about how that went later, but for now I just want to share this clip of me filling time spreading Christmas joy.

This is a party trick that Katie Steckles showed me: you can fold a piece of paper and then make a single cut to produce a five-pointed star. I showed how to do it by following the instructions I’d been told, and then recreated the steps just starting from the insight that when you make the cut, all the edges of the shape need to be on top of each other.

Maybe you’ll show someone else how to do it during the Christmas holiday?

This doesn’t only work for stars: there’s a theorem that you can make any polygon by folding and a single cut. Erik Demaine has made a really good page about the theorem, with some examples to print out and links to research papers. Katie can cut out any letter of the alphabet on demand, which is impressive to witness!

Integer sequence review: A101544

It’s nine years since the first integer sequence review, and six years since the last one. We’ve grown as people, and in CLP’s case, grown people. The world has changed, but our love for the Online Encyclopedia of Integer Sequences hasn’t.


Smallest permutation of the natural numbers with $a(3k-2) + a(3k-1) = a(3k)$, $k > 0$.

1, 2, 3, 4, 5, 9, 6, 7, 13, 8, 10, 18, 11, 12, 23, 14, 15, 29, 16, 17, 33, 19, 20, 39, 21, 22, 43, 24, 25, 49, 26, 27, 53, 28, 30, 58, 31, 32, 63, 34, 35, 69, 36, 37, 73, 38, 40, 78, 41, 42, 83, 44, 45, 89, 46, 47, 93, 48, 50, 98, 51, 52, 103, 54, 55, 109, 56, 57, 113, 59, 60

Presenters wanted: a series of public maths talks by disabled mathematicians

I’m organising a series of online public maths talks through my work, the School of Maths, Stats and Physics at Newcastle University.

The point is that talks will be delivered by disabled presenters. This came about because I and some other disabled people who do maths talks got tired of missing out on opportunities to do outreach because it involves travelling. Not every disability makes travelling harder, but we felt that there were enough people excluded by in-person events that it would be nice to put on a more accessible event.

My aim is for this to take place in December 2022, near to the International Day of People with Disabilities. Talks can be any mathy topic, or about your experience as a disabled mathematician.

I need speakers!

To give some idea of what I’m looking for, I’ll use myself as an example. I count myself disabled at least four ways: I’m colourblind, autistic, dyspraxic, and have Ehlers-Danlos syndrome.

I might talk about:

  • Use of colour in mathematical communication, for example how red chalk makes chalk-and-talks inaccessible.
  • How ambiguously-worded maths problems have stymied me in the past, and how to write them more clearly.
  • Integer sequences, which is just something I’m interested in.

The sessions will be delivered over Zoom, with live captions written by humans and a BSL interpreter. (If you can recommend a BSL interpreter with experience of interpreting maths talks, please get in touch!)

We’ll be advertising the talks to the general public, both grown-ups and schools, so I’m not looking for talks about high-level maths or education research.

This is open to anyone around the world, but if you’re a long way from the UK bear in mind that we’ll schedule the sessions at a convenient time for a British audience.

If you’re interested in taking part, please email

I’d like to have a list of presenters by the end of September, to leave plenty of time to arrange whatever needs to be arranged and to advertise the talks.

Prime Run

Here’s a game I’ve been trying to make for a while.

For a while I’ve had a hunch that there’s fun to be had in moving between numbers by using something related to the prime numbers.

Over the years I’ve tried out a few different ideas, but none of them ever worked out – they were either too easy, too hard, or just not interesting. This time, I think I’ve found something close enough to the sweet spot that I’m happy to publish it.

Prime Run is a game about adding and subtracting prime numbers. You start at a random number, with a random target. Your goal is to reach the target, by adding or removing any prime factor of your current number.

Didn’t Graduate Texts in Mathematics

Every now and then a phrase pops into my head and won’t leave until I write it down or tell it to someone else.

One day the little voice in my head suggested putting “Didn’t” before the classic series of maths textbooks, Graduate Texts in Mathematics.

So I found a cover of a GTIM book, stuck “Didn’t” on the front and changed the title to an in-joke about not understanding category theory, and was happy with my life.

A Springer book cover: Didn't Graduate Texts in Mathematics. Sandy McLane? When All The Arrows Mean It's Obvious

But then I thought that it would make sense to make a whole series of these, so I spent a couple of hours making a meme generator.

And then I tooted and tweeted it.

Now I’m calculating with constructive reals!

A while ago I made myself a calculator. I don’t know if anyone else uses it, but for the particular way I like doing calculations, it’s been really good. You’d think that if a calculator does anything, it should perform calculations correctly. But all calculators get things wrong sometimes! This is the story of how I made my calculator a bit more correct, using constructive real arithmetic.

One thing you need to think about when making a calculator is precision. How precise do the answers need to be? Is it OK to do rounding? If you do round, then it’s possible that errors accumulate as you compose operations.

I’ve always wanted to make a calculator that gives exactly correct answers. This isn’t strictly possible: there are more real numbers than a finite number of bits of memory can represent, or a digital display can show, no matter how you encode them. But I’m not going to use every real number, so I’ll be happy with just being correct on the numbers I’m likely to encounter.