Linkage

A little out of order because it made more sense that way:

• A triangulated polygon, from Les Amusemens Mathématiques by André-Joseph Mancoucke, 1749. Jeff Erickson delves once again into the history of mathematics, to find what might be the first statement of the theorem that every simple polygon has a triangulation.

• The new Dropbox sucks (\(\mathbb{M}\)). At least, it does if all you want is low-fuss synchronization of files between your computers. If you want cloud backup, a resource-intensive desktop app, or easy collaboration between multiple users, it might still be ok for you.

  After getting annoyed with Dropbox’s mission creep and bloat, I’ve started trying syncthing as a replacement (\(\mathbb{M}\), via). It seems like a pretty good replacement, without the bells and whistles that I don’t want or need.

• Abstract aerial photography by JP and Mike Andrews (\(\mathbb{M}\)).

• Godfried Toussaint has died (\(\mathbb{M}\)). Godfried “is considered to be the father of computational geometry in Canada”. This comes as a bit of a shock to me as he seemed healthy enough when I saw him last spring in Barbados. For more, see his memorial web site.

• How should academics cite their transgender colleagues’ work produced under past identities? (\(\mathbb{M}\)). This article has more questions than answers but the advice at the end (when in doubt, ask them what they prefer) seems like a good idea.

• Les Éléments de l’Art Arabe (\(\mathbb{M}\), via). Lots of plates of pretty geometric girih patterns, from an 1879 book by Jules Bourgoin.

• A walk on the wild side: Predatory journals and information asymmetries in scientific evaluations (\(\mathbb{M}\), non-paywalled version, talk slides). A study of which Italian researchers use predatory journals, why, and how prevalent they are. One conclusion surprised me: 40% of Scopus-listed journals show symptoms of being predatory. See also a list of dubious journals aimed at helping Wikipedia editors identify bad sources.

• Limit shapes and affine perimeters (\(\mathbb{M}\)), guest post on Gil Kalai’s blog by Imre Bárány. The affine perimeter of a convex curve is an affine-equivariant number in units of length\(^{2/3}\), zero for polygons and larger for smooth curves. And the limit shape of a convex set is what you get by taking a uniformly random convex subset of a grid within the set, in the limit as the grid becomes very fine; it turns out to be the max-affine-perimeter curve contained in the set.

• Voronoi diagrams + irregular line segment replacement curves + Clojure + SVG + laser cutter = jigsaw puzzles (\(\mathbb{M}\), via).

• Non-concentration of the chromatic number of a random graph (\(\mathbb{M}\), via). Shamir & Spencer ‘87 and Alon & Krivelevich ‘97 proved that random graphs \(G(n,p)\) with \(p=n^{1/2-\varepsilon}\) have almost surely only two possible chromatic numbers. But now Annika Heckel has shown that dense random graphs have a significantly wider spread in colors.

• The Great Wave: what Hokusai’s masterpiece tells us about museums, copyright and online collections today (\(\mathbb{M}\), via). An interesting comparison of different museum policies on re-use of images of their artworks, and availability of high-resolution images, when the art itself is old enough to be out of copyright but photos of the art might still be copyrighted depending on different national laws. The Library of Congress and Rijksmuseum get high marks.

• Helena Verrill’s mathematical/geometric art (\(\mathbb{M}\)), mostly involving arrangements of circles.

• Atomic embeddability, clustered planarity, and thickenability (\(\mathbb{M}\)). Rado Fulek and Csaba Tóth announce a polynomial time algorithm for clustered planarity (given a graph and a hierarchical clustering of its vertices, draw the graph planarly with clusters as simple closed curves and no unnecessary cluster-edge crossings). If this holds up, it’s big: the problem has been open since 1995 and a lot of people have worked on it with only modest progress until now.