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Hallo, new Mastodon users! Here on mathstodon.xyz we've got a couple of mathematical emoji: and . I'd love to add some more. If you can make a PNG image the same size as those, send it to me and I'll add it. Faces of famous mathematicians are an easy place to start; could we have some shapes, polyhedra, or other mathographics too?

I've just released a simple #ActivityPub debugging tool. It's hosted on Glitch so you don't have to worry about spinning up servers or SSL certs etc. You clone your own copy of the project, set it up, and you can create ActivityPub accounts that can send any raw JSON payload you specify to its followers. I use it for testing new and novel ActivityPub objects, and to test compatibility with messages sent from remote servers without needing to create an account on them.

I've made a demo page with an editor, so you can see it and believe it: https://tikzjax-demo.glitch.me

Today: trying to think of use cases for the new 'explore' mode in Numbas. It enables questions where the student can choose what to do next, and subsequent parts depend on answers to previous parts.

At the moment, I've got:

* choose which hypothesis test to do on this data

* how many roots does this equation have -> enter those roots

* ask for subsequent terms of a sequence, until you can write down the formula

Also while I'm picking on Wiley, how did the following paper ever pass peer review for their journal _Concurrency and Computation, Practice and Experience_ (or even a basic sanity check that it has a coherent topic that fits the mission of the journal? https://doi.org/10.1002/cpe.5484

Puzzle problem: Suppose \(A_1, A_2, \ldots, A_n\) are finite sets, and each \(A_i\) contains an odd number of elements. Prove that there is a set \(S\subseteq \left\{1, 2, \ldots, n\right\}\) such that \(\displaystyle\sum_{i\in S} \left|A_i \cap A_j\right|\) is odd for every \(j\in \left\{1, 2, \ldots, n\right\}\).

A puzzle from the MSRI newsletter, Emissary:

"Each of the twelve faces of a dodecahedron has a light that is also an on/off button. Pushing the light causes all five of the lights on the adjacent faces to switch state (go from on to off, or the reverse). Prove that any of the 2¹² positions can be obtained from any other by a suitable sequence of button pushes."

If I'm honest, I'm sharing this because I solved it. I wasn't so clever with the other puzzles.

http://www.msri.org/system/cms/files/973/files/original/Emissary-2019-Fall-Web.pdf

The surprising link between recreational math and undecidability (https://blogs.scientificamerican.com/roots-of-unity/the-surprising-link-between-recreational-math-and-undecidability/): Evelyn Lamb describes how a seemingly isolated fact about Fibonacci numbers (\(F_n^2\vert F_m \Rightarrow F_n\vert m\)) led to Matiyasevich's solution to Hilbert's 10th problem, that there is no general algorithm for solving Diophantine equations.

Slides at http://somethingorotherwhatever.com/baked-sudoku-big-mathsjam-2019/, and an interactive version at https://glass-sudoku.glitch.me/

Braiding gears. Three gears are linked in a chain, but you can “braid” them, rearranging how they connect to each other. Full video at https://youtu.be/Lh7yAbw0H24

seed phrase: Magpie Horse Pheasant Kudu Porcupine (HQ: http://aka-san.halcy.de/quasi/389717597.gif )

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Mathematician, koala fan, mathstodon.xyz admin,

⅓ of https://aperiodical.com

Joined Apr 2017