0xDE @11011110@mathstodon.xyz

This is the Grünbaum–Rigby configuration (https://en.wikipedia.org/wiki/Gr%C3%BCnbaum%E2%80%93Rigby_configuration), three overlaid regular heptagrams with 21 points and lines, 4 points per line, and 4 lines per point. Klein studied it in the complex projective plane in 1879, but it wasn't known to have a nice real realization until Grünbaum and Rigby (1990). Wikipedia editor "Tomo" (I'll let you figure out who that is) started a new article a month ago, and now it's on the front page of Wikipedia in the "Did you know" section.

New blog post: Playing with model trains and calling it graph theory, https://11011110.github.io/blog/2019/05/02/playing-model-trains.html

New blog post: Euler characteristics of non-manifold polycubes, https://11011110.github.io/blog/2019/04/23/euler-characteristics-nonmanifold.html

Regular polygon surfaces: https://arxiv.org/abs/1804.05452
Ian Alevy answers Problem 72 of The Open Problems Project (http://cs.smith.edu/~jorourke/TOPP/P72.html#Problem.72): every topological sphere made of regular pentagons can be constructed by gluing regular dodecahedra together.

You can also glue dodecahedra to get higher-genus surfaces, as in this image from https://momath.org/mathmonday/the-paragons-system/, but Alevy's theorem doesn't apply, so we don't know whether all higher-genus regular-pentagon surfaces are formed that way.

New blog post: Monochromatic grids in colored grids, https://11011110.github.io/blog/2019/04/14/monochromatic-grids-colored.html

New blog post: Coloring kinggraphs, https://11011110.github.io/blog/2019/04/11/coloring-kinggraphs.html

A 3-regular matchstick graph of girth 5 consisting of 54 vertices (https://arxiv.org/abs/1903.04304), Mike Winkler, Peter Dinkelacker, and Stefan Vogel. The previous smallest-known graph with these properties had 180 vertices, but this one might still not be optimal, as the known lower bound is only 30. I found it difficult to understand the connectivity of the graph from its matchstick representation so I added another drawing in a different style.

New visualization of the shockwaves created by supersonic aircraft, created by NASA using aerial schlieren photography and stunt piloting: https://arstechnica.com/science/2019/03/nasa-visualizes-supersonic-shockwaves-in-a-new-awe-inspiring-way/

Time to get a new keyboard. If I've been even more unresponsive online than usual this week, this is why. Fortunately the Apple Keyboard Service Program https://www.apple.com/support/keyboard-service-program-for-macbook-and-macbook-pro/ came through, and now my laptop looks and feels good as new.

This is YBC 7289, a Babylonian tablet from 1800 BC – 1600 BC showing the sides and diagonals of a square with a very accurate sexagesimal approximation to the square root of two, "the greatest known computational accuracy ... in the ancient world". Now a Good Article on Wikipedia, https://en.wikipedia.org/wiki/YBC_7289

The Cal Poly ag students have started selling these blood oranges at the local farmer's market, as they do every year around this time, only $1 for five. In the summer they sell sweet corn on the cob.

Holes and their reflections. (The reflections are in the curved surface of an espresso portafilter.)

The view from my desk. Actually my office has lots of windows with a nice view of a well-used plaza, outdoor coffee shop, trees, and distant mountains. But to see that, I have to get up and go over to one of the windows. If I stay at my desk and look up at the window, I see this interesting geometric pattern instead.

This is not a cinnamon bun. It's actually a 160 million year old fossil snail shell from Madagascar, roughly the size of a large fist (or cinnamon bun). I don't think it's particularly rare or valuable; I picked it up because I liked its shape.

Spotted on the Cambridge University Press display table at SODA...

Matsya And The Great Deluge, street art from Fort Bragg illustrating an ancient Indian folk tale. For a more complete view of this piece and more information about it, see https://www.fortbraggalleywayart.org/the-fish-mural.html

It feels like I haven't been taking and posting enough photos. So here's a cell phone shot from yesterday that I took to illustrate the Wikipedia article https://en.wikipedia.org/wiki/Mendocino_Beacon

The Beacon hasn't actually lived there for nearly 20 years, but their old sign still hangs on the building.

Amazon trained a sexism-fighting, resume-screening AI with sexist hiring data, so the bot became sexist: https://boingboing.net/2018/10/11/garbage-conclusions-out.html

A Problem Fit for a Princess: https://www.mathteacherscircle.org/news/mtc-magazine/sa2017/apollonian-gaskets/

A post on the history of the Apollonian Gasket, a fractal formed by tangent circles, inspired by its use as the logo of the San Joaquin Math Teachers’ Circle.