Animation of the minimum-weight matchings of increasingly many points of two colors in a unit square: twitter.com/thienan496/status/

Because the color densities fluctuate, the matching develops regions of many parallel long edges transporting excess density from one place to another. This is reflected mathematically in the fact that the expected length is \(\Theta(\sqrt{n\log n})\) compared to \(\Theta(\sqrt{n})\) for non-bipartite matching; see doi.org/10.1007/BF02579135

Render onto Caesar the texture map that is Caesar's

Hanlon's razor for identical incorrect exam answers: never attribute to collusion that which is adequately explained by synchronised stupidity.

Rick Astley will let you borrow any of his Pixar DVDs, except one

The existence of pronouns implies that all other nouns are merely amateur nouns

Because of Euler we know that for polyhedra without holes we have
V+F=E+2. As a result we can't have a polyhedron made entirely of
hexagons, and need at least 12 pentagons or an equivalent set of
shapes. Etc.

But things change if we allow intersecting faces. Clearly we have
a lot of scope for variations, but we can always retain limits to
make things reasonable.

But ...

Can we make a "polyhedron" consisting only of hexagonal "faces"?

Brains are weird. I spent half a minute today trying to figure out why the phrase "go to the dentist" reminded me of Star Wars.

The four points, two distances problem: theguardian.com/science/2019/o

Can you find all of the ways of arranging four distinct points in the plane so that they form only two distances? The link is not a spoiler but it has a separate link to the solution. "Nearly everyone misses at least one" says Peter Winkler; can you guess the one I missed?

Because I just spent 15 minutes trying to remember how to find out what variables a CMake find_package call sets:

cmake --help-module Find<name>

Goddammit. Why is this information so hard to find?

Robert MacKay's Chaos Machine. Its configuration space is a genus three surface. The dynamics of the machine are equivalent to geodesic flow on the surface, which is Anosov, hence chaotic.

The problem with transiting though Shanghai airport is that all the staff try to talk to me in Chinese

I sure do love when the metro makes an announcement they say only once so by the time you start paying attention all you catch is "The inconvenience is regretted"

Compact packings of the plane with three sizes of discs: arxiv.org/abs/1810.02231, Thomas Fernique, Amir Hashemi, and Olga Sizova

Here, "compact packing" means interior-disjoint disks forming only 3-sided gaps. The circle packing theorem constructs these for any finite maximal planar graph, with little control over disk size. Instead this paper seeks packings of the whole plane by infinitely many disks, with few sizes. 9 pairs of sizes and 164 triples work. Here's one from Fig.3 of the paper.

shitpost about 90s TV 

Do Scandanavians pronounce the STARGÅTE logo as "star goat"?

Here's a 1965 RAND report demonstrating a conversational interface with an algebraic processing system. They determine that a conversational user interface vastly improves usability in their tests.

Full PDF: rand.org/content/dam/rand/pubs

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Of course Mac OS X's Calendar interprets "IST" as Irish Standard Time and not Indian Standard Time. The fool is me for expecting different.

I got the urge to start singing "Domo Arigato Mr. Roboto" the moment I landed in Tokyo and I'm pretty sure that's extremely culturally insensitive

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