Pinned toot

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

Pinned toot

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...>

Pinned toot

@jordyd

"...now lastly, set \(x=10\), ..."

Pinned toot

#proofinatoot 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! https://youtu.be/9T3zCsyx98g

Origametry: Mathematical Methods in Paper Folding (https://www.cambridge.org/us/academic/subjects/mathematics/recreational-mathematics/origametry-mathematical-methods-paper-folding), 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 (https://books.google.com/books?id=LdX7DwAAQBAJ), but it looks interesting and worth waiting for.

Closed quasigeodesics on the dodecahedron (https://www.quantamagazine.org/mathematicians-report-new-discovery-about-the-dodecahedron-20200831/), 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: https://arxiv.org/abs/1811.04131, https://doi.org/10.1080/10586458.2020.1712564

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.

https://cornelllabofornithology.github.io/auk/

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

https://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: http://arxiv.org/abs/1907.08726v2

PDF: http://arxiv.org/pdf/1907.08726v2

Entry: https://read.somethingorotherwhatever.com/entry/AnOptimalSolutionfortheMuffinProblem

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"

Show thread

Untangling random polygons: https://sinews.siam.org/Details-Page/untangling-random-polygons-and-other-things

Repeatedly rescaling midpoint polygons always leads to an ellipse.

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: https://docs.google.com/forms/d/e/1FAIpQLSeT4ZWL5iEiYulx72qpBR3zFfmGOoX-6OSXX_D-tL3aps57rw/viewform

More about the conference: https://scholar.social/@bgcarlisle/104546635883635979

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.

- website
- https://bmreiniger.github.io

Combinatorist (esp. graph theorist) turned Data Scientist

Joined Jun 2017