Linkage

Scripted Movement Drawings Series 1 (via). Andrew Kudless makes generative art by programming a robot arm to use a calligraphy brush.

John Baez observes that packing the plane by squares and regular heptagons is much more efficient than packing heptagons alone, and asks where the packing came from (G+). Maybe from the truncated Cairo pentagonal tiling? But there’s another packing (below) by regular pentagons and regular heptagons, that I think is even more efficient. If you tightened it up a little bit to make an actual tiling, it would be difficult to tell that the tiles are not regular polygons. (See G+ comment thread for tightened version and basketweave version.)

Carl Størmer (G+). Another newly promoted Wikipedia Good Article. Størmer was a number theorist, astrophysicist, and amateur street photographer. My favorite result of his is Størmer’s theorem, which provides a method based on Pell equations for finding pairs of consecutive smooth numbers like 80 and 81; I wrote about implementing it in an earlier post.

Proceedings of the 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018; G+).

A mysterious duality relation for 4-dimensional polytopes, by Gil Kalai.

Using circle packings to generate hyperbolic tilings of fractals (G+, via).

The EU’s copyright proposal is extremely bad news for everyone, even (especially!) Wikipedia (via, also via). This proposed law would require Wikipedia and other publishers of user-submitted content to pay for, install, and run expensive commercial filter software that automatically checks all submissions against a database of commercial content and automatically blocks any matches. There would be no safeguards against the already-rampant abuse of such filters to claim copyright on things that are not copyrighted. The article notes that “The drafters of Article 13 have tried to carve Wikipedia out of the rule, but thanks to sloppy drafting, they have failed: the exemption is limited to “noncommercial activity”. Every file on Wikipedia is licensed for commercial use.”

Congratulations octor Chang! Hsien-Chih Chang (a student of Jeff Erickson) successfully defends his thesis on Tightening Curves and Graphs on Surfaces.

Why de-anonymizing peer review might not be a good idea (G+, via). If the reviewer is a woman, it might cause her review to be taken a lot less respectfully than if it were anonymous.

Gabriel Orozco’s Mapa estelar en árbol, 2009 (G+). If you like this, or Orozco’s other pieces involving circle and sphere tangencies, there’s plenty more in his book Orbita Nocturna. I picked up a copy the last time I visited MOCA.

Down in the depths on Carathéodory’s theorem (via). David Orden describes some new connections between two notions of how central a point is to a sample, from robust statistics: Tukey depth (points that can’t be separated by a line from most of a sample set) and Tverberg depth (points that can be surrounded by many disjoint subsets of a sample set). Based on a recent paper by Fabila-Monroy and Huemer.

Hercules’ Dog Discovers Purple Dye. This painting by Rubens shows the wrong kind of snail shell. It should be a dye murex, but it looks more like a nautilus, which is not even actually a snail.

Unique Weathering Pattern Creates Fascinating Geometric Ripples on a Chain Link Fence (G+, via). It looks like a reaction-diffusion system, but it’s not clear what’s reacting and diffusing.

Gödel, Escher … what?. Greg Egan makes five-dimensional shapes with ten different two-dimensional shadows.

The conference of the (American) Association for Asian Studies, located in India, is banning participation by Pakistanis and by other scholars of Pakistani descent (G+). I’m sure it’s possible to point to many similar situations for other combinations of countries; for instance, for several years it has been difficult or impossible for scholars based in Iran to attend US-based conferences. But there should be no place for discrimination or exclusion based on ethnicity, gender, religion (or its absence), or national origin, in the activities of any legitimate scholarly discipline.