Linkage

Closed quasigeodesics on the dodecahedron (\(\mathbb{M}\)), 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:1811.04131, doi:10.1080/10586458.2020.1712564. I saw this on Numberphile a few months back (video linked in article) but now it’s on Quanta.

Lorenz Stöer’s geometric landscapes (\(\mathbb{M}\)). In 2014 I linked a different page with a few of Stöer’s 16th-century proto-surrealist combinations of landscape and geometry, but they were black and white. This one has more of them, in color.

Ideal polyhedron, a polyhedron in hyperbolic space with all vertices at infinity, and Sylvester–Gallai theorem, that every finite set of points in the Euclidean plane has a line that either passes through all of them or through exactly two of them. Both newly promoted to Good Article status on Wikipedia (\(\mathbb{M}\)).

Escherian wiener-dog Cerberus fetches three impossible things.

Flamebait post of the day: Why mathematicians should stop naming things after each other (\(\mathbb{M}\), via). For once the via-link discussion is worth reading (main point: the alternative, using common English words to describe specialized technical concepts, can be even more confusing).

Early Renaissance painter Piero della Francesca was also an accomplished mathematician, and his book on polyhedra, De quinque corporibus regularibus (subject of a new Wikipedia article; \(\mathbb{M}\)) has an interesting history that deserves to be better known. Rediscovery of the mathematics of Archimedes! “First full-blown case of plagiarism in the history of mathematics” (by Luca Pacioli, in Divina proportione)! Maybe owned by John Dee! Long lost and found centuries later in the Vatican Library!

Peter Cameron gives a nice roundup of two recent online conferences on group theory and combinatorics (\(\mathbb{M}\)) that he attended more-or-less simultaneously, something that would have been impossible for physical conferences. The parts on synchronizing automata and twin-width particularly caught my attention as stuff I should look up and find out more about.

An hourglass that demonstrates Archimedes’ theorem that the volume of a cylinder is the sum of the volumes of its inscribed sphere and cone (\(\mathbb{M}\)), from Rod Bogart’s twitter feed.

The hexagon-minimizing simple bipartite polyhedra of my recent blog post make nice shapes when converted to simple orthogonal polyhedra (\(\mathbb{M}\)): a squared-off amphitheater with L-shaped terraces of increasing length as they rise, or a diagonal staircase with congruent L-shaped steps. In each case the outer \(2n\)-gon is the underside of the polygon and the inner cycles are the horizontal faces.

Open is not forever: a study of vanished open access journals (\(\mathbb{M}\), via, via). This study shows the need for systematic archiving and redundant copying of online open journals, but I suspect that the problem for small hand-run print-based journals without much library pickup might be much worse.

A prickly structure made of 70,000 reusable hexapod particles (\(\mathbb{M}\)). Sort of like those seawalls they build by jumbling together giant concrete caltrops, only with pieces that are not quite so big and with usable spaces left void within it. Sometimes the article says “hexapod” and sometimes “decapod”; the pictures appear to show structures that mix two different kinds of particle.

Combinatorial Theory (\(\mathbb{M}\), see also), a new open-access combinatorics journal formed from the mass resignation of the Elsevier JCTA editorial board.

Trump officials are now telling their supporters to buy guns and ammunition to use against scientists for being anti-Trump. No, seriously (\(\mathbb{M}\)).

Origametry: Mathematical Methods in Paper Folding (\(\mathbb{M}\)), new book coming out October 31 by Tom Hull. I haven’t seen anything more than the blurb linked here and the limited preview on Google Books, but it looks interesting and worth waiting for.