Linkage

Diana Davis’s beautiful pentagons (\(\mathbb{M}\)). I briefly mentioned her regular-pentagon billiards-trajectory art in an earlier post but now Evelyn Lamb has a much more detailed column on her and her work.

Points and lines (\(\mathbb{M}\)). A new review of my book Forbidden Configurations in Discrete Geometry, by Daniel Kleitman, in Inference.

About photos of Emmy Noether (\(\mathbb{M}\)), in which Peter Roquette apologizes for having indirectly caused Margaret Tent’s young-adult historical-fiction about Noether to have a photo of someone else on its cover. Via MarkH₂₁ on Wikipedia, in the context of a discussion of the provenance of a different photo of Noether.

The Conway knot is not slice (\(\mathbb{M}\)). Newly published result by Lisa Piccirillo in Ann. Math., with an overview of the significance of the result (if not much of its detail) in Quanta.

Tim Gowers relates the convoluted history of a mathematical announcements journal (\(\mathbb{M}\)). Electronic Research Announcements of the AMS (founded 1995) moved to the American Inst. of Mathematical Sciences in 2007, but recent heavyhanded moves by the publisher led the editorial board to quit, and its name changed to Electronic Research Archive. In the meantime the old editorial board have a new journal: Mathematical Research Reports. See the Gowers link for details.

In preparation for time travel week in graduate data structures, here’s a listicle of 20 time travel movies (\(\mathbb{M}\)). There are any number of these lists but for me they should include at least 12 Monkeys, Primer, Safety Not Guaranteed, Donnie Darko, and Time Bandits. This one adds The Girl Who Leapt Through Time, also good. I’d have thrown in The Infinite Man but it’s obscure enough that I’m not offended by its absence. The relevant one for my class, Retroactive, can stay off.

Spirals and loops twist through wooden sculptures by Xavier Puente Vilardell (\(\mathbb{M}\)).

Dmitri Panov constructs infinitely many convex 4-polytopes with no triangle or quadrilateral 2-faces (\(\mathbb{M}\)). The construction is pretty: take some 120-cells (all 2-faces regular pentagons and all 3-faces regular dodecahedra), embedded into hyperbolic space so all dihedrals are right angles, and glue them together on shared facets. If at most two touch at each ridge, the result is convex. Some pairs of pentagons merge into hexagons, but you still have no triangles or quads.

Ten things you (possibly) didn’t know about the Petersen graph (\(\mathbb{M}\)). Found while making a Wikipedia article on the book The Petersen Graph (for the graph itself, see its Wikipedia article).

Godfried Toussaint’s book The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good?, on the mathematical analysis of drumming patterns, has a new expanded posthumous 2nd edition (\(\mathbb{M}\)). I was able to download free from there but that may be via a campus subscription; your access may vary. For a description of the 1st edition of the book (probably undetailed enough that it can describe the 2nd as well) see its Wikipedia article.

French video about self-replicating patterns in cellular automata, with English subtitles (\(\mathbb{M}\), via).

@erou visualizes the complexity of Karatsuba’s algorithm for integer multiplication as a Sierpiński triangle, inside a square, with a number of dark pixels proportional to the steps of the algorithm. The square itself counts in the same way the complexity of the naive algorithm.

Republicans propose legislation to bar Chinese from science (\(\mathbb{M}\)). I’m having difficulty distinguishing this sort of move from “Nazis propose legislation to bar Jews from science”.

Arthur C. Clarke and the projective plane (\(\mathbb{M}\)). Wrog beanplates Clarke’s “The Wall of Darkness” (1949).

Volumes of projections of unit cubes (\(\mathbb{M}\)), Peter McMullen, Bull LMS 1984. A cute theorem that deserves to be better known: if you hold a unit cube in the noonday sun, at any angle, its shadow’s area equals its height (elevation difference between lowest and highest point). It follows immediately that the biggest possible shadow is a hexagon with area = long diagonal length = \(\sqrt{3}\), and the smallest shadow is a unit square. Similar things happen in higher dimensions.

Meander, a procedural system for generating historical maps of rivers that never existed (\(\mathbb{M}\), via). The way this system models the motion of river beds over time looks a lot like the time-reversal of the curve-shortening flow, but with added tangential motion that causes bends to flow downstream (and maybe helps maintain smoothness) and with shortcutting of oxbows.