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Anyone hear of this before, or can find something about it? It seemed kinda cool at the time, and I like this axiomatization.

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Background: A finite projective plane has point-line duality, and affine planes lack it. You can get a projective plane by adding a "line at infinity," and this is reversible.

Years ago I stumbled across this in constructing a counterexample to a graph conjecture, and I never found out if it was something people had realized or used before:
We can also recover point-line duality from an affine plane by just deleting one of the parallel classes of lines. <cont...>

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@jordyd
"...now lastly, set $$x=10$$, ..."

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that if a finite poset has a unique maximal $$x$$, then $$x$$ is maximum.

If not, there is a $$y_1||x$$. $$y_1$$ is not maximal, so there is $$y_2>y_1$$; we cannot have $$y_2<x$$, else transitivity would give $$y_1<x$$, and we cannot have $$y_2>x$$ because $$x$$ is maximal, so $$y_2||x$$. Continuing, we build a chain $$y_1<y_2<\dotsb$$ (with $$y_i||x$$ for all $$i$$), contradicting finiteness.

(This proof also suggests a construction of an infinite poset without the property.)

The dLX (pronounced "d-Lex", as in "lexicon"), is a new 60-sided, alphabetical die from The Dice Lab. Sixty is enough for us to get a letter distribution that is close to the distribution in the English language, so they can be used for word search games! youtu.be/9T3zCsyx98g

Origametry: Mathematical Methods in Paper Folding (cambridge.org/us/academic/subj), new book coming out October 31 by @tomhull

I haven't seen anything more than the blurb linked here and the limited preview on Google Books (books.google.com/books?id=LdX7), but it looks interesting and worth waiting for.

Preparing the maths can be a mess.
Hope the talk will not be one.

Tired: Necessary evil
Wired: Necessary and sufficient evil

Closed quasigeodesics on the dodecahedron (quantamagazine.org/mathematici), paths that start at a vertex and go straight across each edge until coming back to the same vertex from the other side. Original paper: arxiv.org/abs/1811.04131, doi.org/10.1080/10586458.2020.

I saw this on Numberphile a few months back (video linked in article) but now it's on _Quanta_.

The Cornell Lab of Ornithology has an R frontend to awk, called auk.
cornelllabofornithology.github

mathstodon.xyz now has a live preview and completion of LaTeX!
This has been on my to-do list for a long time. You no longer need to worry if LaTeX will display properly or not.

Nice little bit of card-shuffling mathematics, but also an excellent presentation that takes advantage of the medium.
fredhohman.com/card-shuffling/

New entry!
An Optimal Solution for the Muffin Problem
Article by Richard E. Chatwin
In collections: Attention-grabbing titles, Food, Fun maths facts, Protocols and strategies
The muffin problem asks us to divide $$m$$ muffins into pieces and assign each of those pieces to one of $$s$$ students so that the sizes of the pieces assigned to each student total $$m/s$$, with the objective being to maximize...
URL: arxiv.org/abs/1907.08726v2
PDF: arxiv.org/pdf/1907.08726v2

I need help finding the hole in this argument...

Let K be a CM number field, K+ its maximal real subfield, k the 2-part of K with subfield k+ likewise. Suppose K has a purely imaginary unit a. Then by Remak [1], a is of the form \sqrt{-u} for a totally positive non-square unit u of K+. The degree of K over k is odd, therefore the norm N_{K/k}(a) is also purely imaginary, and a unit. Therefore a totally positive non-square unit exists in k+, and moreover it is found similarly.

baby highland cow pics, cow eye contact

i was taking pictures of it and it was like "oh? you desire a Model? well let me come closer"

The set of all sets which don't contain themselves is coming from inside the set 😳

Untangling random polygons: sinews.siam.org/Details-Page/u

Repeatedly rescaling midpoint polygons always leads to an ellipse.

Ah, the two genders:
- tautological
- vacuous

We start warning 'no mask' like 'eye contact' on selfies when.

It's 5/8, or Almost The Worst Approximation to Φ day!

Is there a term for an $n$-regular graph which can have its vertices $n$-colored so that each vertex has all $n$ colors among its neighbors? (For example, a cycle whose length is a multiple of 4 works for n=2, and the triangular prism for n=3).

So, I know you know this by now, BUT: scholar.social are hosting a mini-conference! All sorts of disciplines and a lovely line-up of talks.

To get the links so you know when the talks are and what vidchat to drop in on for them, sign up here: docs.google.com/forms/d/e/1FAI

Let $$K$$ be a cyclic number field over $$\mathbb{Q}$$ of degree $$q=7$$ with Galois group $$G$$ and consider the $$\mathbb{F}_2$$ algebra over $$G$$, also known as the group ring. This is isomorphic to $$\mathbb{F}_2[x]/(x^q+1)$$. In the case $$q=7$$, the ideal $$(x^q+1)$$ splits mod $$2$$ as $$(x-1)(x^4+x^2+x+1)(x^4+x^2+x)$$. So even though the Galois group is cyclic, the $$\mathbb{F}_2$$ algebra over it is not.

How to be a mathematician:

Definition: An object that does what we want.

Example: Some objects don't do what we want.

Definition: An object is called normal if it *really* does what we want.