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 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.

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.

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I'm a computer scientist at the University of California, Irvine, interested in algorithms, data structures, discrete geometry, and graph theory.

Joined Apr 2017