Pinned toot

@christianp I do not own the number 5, the aperiodical logo, or a nice assortment of classroom furniture.

But the fog on the Tyne is all mine.

I've updated my maker to prompt for image descriptions, and to show you suggested alt text for the final image.
Suggestions for a better format for the alt text are welcome!

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Truth is subjective.
The children think I've put a climbing frame in the garden.
From my perspective, I've increased the genus of my mowing surface.

My first toot about this contained an example using pictures of humans. A couple of people rightly pointed out that that could lead to some unwanted reactions to the prompt, which I hadn't realised. I've deleted it, so here's another attempt

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I've made a tool for making "Which One Doesn't Belong?" pictures.

You can put text or pictures in each square, and change the colours of the background and text.

wodb-maker.glitch.me/

Today I've made my first contribution to MathJax in almost three years, adding the ability to specify a 'nonce' value for the stylesheets it creates, to comply with the site's Content Security Policy.
I've got an issue on the MathJax issue tracker explaining in a bit more detail: github.com/mathjax/MathJax/iss

In particular, this makes MathJax work in mastodon again.

Do you have a favourite integer sequence in the OEIS? If so, what is it?

(boosts appreciated)

@christianp I remember a conference talk on the proof that braid groups are linear. The presenter explained that his proof would use "forks and noodles," and went on to clarify that "noodles" are embedded arcs that represent certain cohomology classes, and "forks" are, "...um, what you use to detect noodles."

Mathematicians: the first step in solving a problem is to write your problem out in the simplest terms you can.

Also mathematicians:

A game for two players: you each pick a real number between in the interval [0,1]. Whoever picks the highest number wins. If you both pick the same, you go again.
Play three times. You can't pick the same number more than once.

Is there a strategy?

@christianp Because then all the physicists like me would confuse it with "six-bar", which is six over two pi

You know how wise people put crosses through their handwritten 7s and 0s to differentiate them from 1s and Os?
Why don't we put a cross through a 6 so you can tell it apart from an upside down 9? Like ð but flipped

I came across this nice integerological fact:

Define \(\operatorname{ord}_p(n)\) to be the power of \(p\) in the prime factorisation of \(n\).

Then

\[ \sum_{k=1}^n\gcd(n,k) = \prod_{p|n} \left(1+\left(1-\frac{1}{p}\right) \cdot \operatorname{ord}_p(n)\right) \]

I don't know why you'd want to do this, and all the references I've found to it talk about it as a special case of some more general identities, but for some reason it appealed to me.

Here's something you can do without thinking, assuming you've had the same realisation I've just had:

Write down a multiple of 2¹⁰⁰

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