@cerisara You're welcome!

I guess not, since this is additionnal feature from mathstodon.xyz.

I use @fedilab (which is great) on my phone and it does not work.

But you also have other features that allow you to type math in unicode, and in that case it works with a phone.

Like \mathbb{Z} becomes ℤ on mathstodon.xyz; same goes for ℚ, ℝ... You also have upperscript and subscript with ^3 = ³ and _9 = ₉ and greek letters \alpha = α. Try it! 🙂

It's well known that \( |\mathbb{N}| = |\mathbb{N}^2| \) and it's not hard to make an explicit 1-1 mapping. Ditto \( |\mathbb{Q}| = |\mathbb{Q}^2| \).

We also know that \( |\mathbb{R}| = |\mathbb{R}^2| \).

Your challenge, should you decide to accept it, it to give an explicit one-to-one mapping.

Go ...

oops, just noticed I forgot to tag @11011110 in the above toot, for making that diagram. Follow him!

How do you convey non-hamiltonianicity? I've got flocks of boids endlessly trying to trace out the graph. They're chasing (invisible) rabbits which are randomly walking the graph.

There's an easy proof of this: you can colour the vertices red and blue so that no vertices joined by an edge are the same colour, and there are an odd number of vertices.

So any lap visiting each vertex once has to end on a different colour to the start.

Here's an image showing the colouring property, by David Eppstein. If you start on blue, you have to finish on red, and vice versa.

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It's the smallest non-Hamiltonian polyhedral graph - you can't draw a path on it which visits each vertex exactly once, and it corresponds to a polyhedron.

There's no such thing as a "lap" of this graph which doesn't cross itself somewhere.

Another one. Here, flocks of arrowheads are tracing out the Herschel graph.

The Herschel graph is something I keep returning to, because our building is named after its inventor.

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I wanted it to have a dark background so it would look like writing on a blackboard, but I was told I can't print a 99% black page at A0.

Eventually, I want to put the original handwriting samples on the school website, along with links to the authors' homepages and short explanations of what they're about.

I learnt a lot about what my colleagues do just by asking them to write a line or two of #math!

To make this, I took photos of all the handwriting samples, then used #inkscape to convert them to vector images. I separated out individual characters, then wrote code to lay characters along line segments making up a hexagon tiling.

My idea was to have something that gives you an idea of notation used by mathematicians, but better than the 'cumulonumbers' nonsense you normally get.

There's just enough coherence to identify subdisciplines, but I didn't worry about keeping whole formulas intact.

Here's a closeup of the handwriting one. I wandered round the department knocking on doors, asking people to write some mathematical notation. It was fascinating seeing the different symbols and conventions used in different disciplines.

What can you spot in this snippet?

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Art* is going on walls!

On the right is one of the Truchet pieces I shared above, and the other is made up of handwriting samples I gathered from colleagues. It feels good to finally put something out with this!

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A big list of unlikely or surprising Turing-complete systems: https://www.gwern.net/Turing-complete, via https://www.metafilter.com/183095/On-having-sufficient-complexity-to-allow-for-arbitrary-computation

My favorite: SVG is Turing-complete because it can be used to (slowly) simulate Rule 110 (and one hopes the weird boundary conditions needed to make Rule 110 Turing complete): https://github.com/tom-p-reichel/svg-is-turing-complete

https://www.thingiverse.com/thing:3856293

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Mathematician, koala fan, mathstodon.xyz admin,

⅓ of https://aperiodical.com. He/him

Joined Apr 2017