This is YBC 7289, a Babylonian tablet from 1800 BC – 1600 BC showing the sides and diagonals of a square with a very accurate sexagesimal approximation to the square root of two, "the greatest known computational accuracy ... in the ancient world". Now a Good Article on Wikipedia, en.wikipedia.org/wiki/YBC_7289

New blog post "Mutual nearest neighbors versus closest pairs" (11011110.github.io/blog/2019/0), introducing my latest arXiv preprint, "Euclidean TSP, Motorcycle Graphs, and Other New Applications of Nearest-Neighbor Chains" (with Efrat, Frishberg, Goodrich, Kobourov, Mamano, Matias, and Polishchuk, arxiv.org/abs/1902.06875)

@bremner Despite seeing so little of it in your shot, that looks like a familiar setting.

You can't pack uncountably many Möbius strips into 3d space: quantamagazine.org/mobius-stri

Known since the early 1960s for polyhedral embeddings, this has been recently generalized to arbitrarily messy topological embeddings, and to higher dimensions, in two papers doi.org/10.1142/S0218216518420 by Olga Frolkina and arxiv.org/abs/1810.04089 by Sergey Melikhov.

Paul Erdős died in 1996, but his most recent paper is from 2015, nearly 20 years later! There's a writeup at simonsfoundation.org/2015/12/1; the paper itself is math.ucsd.edu/~ronspubs/pre_tr

It's about Egyptian fractions – representations of rationals as sums of distinct unit fractions – and is motivated by the conjecture that it's always possible for all denominators to be semiprime. That's still open, but they prove that every integer has a representation with all denominators products of three primes.

@RefurioAnachro Thanks for the fixed link. I had saved it for later reading but hadn't gotten to it yet so didn't notice. \(\mathbb{F}_1\) is always fun...

A comparison of two parallel Canadian grant funding tracks shows that when reviewers are told to focus on the investigator rather than the proposed investigation, they are significantly more biased against women: cbc.ca/news/health/cihr-gender

Choose a random graph with countably infinite vertices by flipping a coin to decide whether to include each edge. Or, construct a graph with binary numbers as vertices, with an edge \(x\)—\(y\) when \(x<y\) and the \(x\)th bit of \(y\) is one. Or, construct a graph on primes congruent to 1 mod 4, with an edge when one is a quadratic residue mod the other. They're all the same graph, the Rado graph (en.wikipedia.org/wiki/Rado_gra)! It has many other amazing properties. Now a Good Article on Wikipedia.

Elsevier news roundup: German, Hungarian, and Swedish academics have been cut off from Elsevier journals after subscription negotiations broke down (nature.com/articles/d41586-019). Negotiations with the University of California are ongoing after a missed deadline (insidehighered.com/quicktakes/). Access to Germany was restored (nature.com/news/german-scienti) but without any long-term agreement. And the editorial board of _Informetrics_ resigned to protest Elsevier's open access policies (nature.com/articles/d41586-019).

The list of accepted papers from this year's Symposium on Computational Geometry just came out: eecs.oregonstate.edu/socg19/ac

Four of Conway's five $1000-prize problems (oeis.org/A248380/a248380.pdf) remain unsolved:

*The dead fly problem on spacing of point sets that touch all large convex sets, en.wikipedia.org/wiki/Danzer_s

*Existence of a 99-vertex graph with each edge in a unique triangle and each non-edge the diagonal of a unique quadrilateral, en.wikipedia.org/wiki/Conway%2

*The thrackle conjecture, on graphs drawn so all edges cross once, en.wikipedia.org/wiki/Thrackle

*Who wins Sylver coinage after move 16? en.wikipedia.org/wiki/Sylver_c

@jsiehler @axiom If it has a name or prior publications I don't know about it. But it reminds me of several other more well-studied concepts:

* partial cubes (label vertices by bitstrings, not necessarily using all strings, so that Hamming distance = graph distance)

* graceful graphs (label vertices by numbers so that the differences of labels on the endpoints of each edge are the numbers from 1 to )

* Tutte embedding, each vertex is centroid of neighbors en.wikipedia.org/wiki/Tutte_em

0xDE boosted

Three-regular, each 5-bit label appears exactly once, each vertex is the sum (xor) of its neighbors.

@jsiehler Any idea whether you can label the Dyck graph (en.wikipedia.org/wiki/Dyck_gra) in the same way? Or is it just this graph?

0xDE boosted

Finished my stained glass course, and the Menger sponge piece I was making over the course of it. Really, really happy with the results, and to have learned about this medium; the whole process was interesting and I wrote about it (with lots of pictures) here:

joshmillard.com/sgmenger/

#art #fractal

Did you know that two different graphs with 81 vertices and 20 edges/vertex are famous enough to have Wikipedia articles?

The strongly regular Brouwer–Haemers graph (en.wikipedia.org/wiki/Brouwer%) connects elements of GF(81) that differ by a fourth power.

The Sudoku graph (en.wikipedia.org/wiki/Sudoku_g) connects cells of a Sudoku grid that should be unequal. Sudoku puzzles are instances of precoloring extension on this graph.

Unfortunately the natural graphs on the 81 cards of Set have degree ≠ 20...

"Ancient Turing Pattern Builds Feathers, Hair — and Now, Shark Skin": _Quanta_, quantamagazine.org/ancient-tur and original article in _Science Advances_, doi.org/10.1126/sciadv.aau5484

Researchers at the University of Florida led by Gareth Fraser and his student Rory Cooper used reaction-diffusion patterns (also named "Turing patterns" after Turing's early work; see en.wikipedia.org/wiki/Turing_p) to model the distribution of scales on sharks, and performed knockdown experiments to validate their model in vivo.

The Cal Poly ag students have started selling these blood oranges at the local farmer's market, as they do every year around this time, only $1 for five. In the summer they sell sweet corn on the cob.

@janne Your response still demonstrates a lack of having read the article, because it raised exactly this argument as a straw man, only to point out that the same reviewer is free to continue doing the same thing at other journals.

Show more
Mathstodon

A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.

Use \( and \) for inline LaTeX, and \[ and \] for display mode.