New blog post: Portland street art,

I’ve been in Portland, Oregon this week for Computational Geometry Week. Here are a few photos of local street art, the first set I’ve taken with my new Pixel 3 XL cellphone (I neglected to bring an actual camera for this trip).

Squaring the spherical earth:

For surveying purposes, Orange County is divided into "sections", typically 1 mile² (not axis-aligned!) with small brass markers at their corners. One corner lands in the UCI faculty housing development where I live, and the housing association took the opportunity to make a larger decorative marker for it. It's on a sidewalk between my house and the farmer's market, so I happened to walk past it this week.

New blog post: Dancing arc-quadrilaterals,

In which an analogy to Matisse's ring of abstracted dancing figures lets me prove the nonexistence of Lombardi-style graph drawings for certain bipartite planar graphs and series-parallel graphs.

Square wave patterns in nature: (where this image comes from)

And wave patterns in social media: search for "cross sea" and note its appearance on gizmodo in 2014, amusingplanet in 2015, azula in 2017, providr in 2018, sciencealert in 2019...all repeating the same somewhat garbled explanation of mathematical wave models and danger to shipping.

Compact packings of the plane with three sizes of discs:, 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.

Line arrangements in architecture: the beams of Cambridge's Mathematical Bridge ( form tangent lines to its arch and then extend through and support its trusswork, while another set of radial lines tie the structure together.

The bridge just looks like a wood truss bridge in real life but this artificially-colored image, from, makes the underlying structure clearer.

The UCI University Club (which in other places might be called a faculty club) is next door to the building I work in, and has a bustling side business hosting weddings. Here's the view that greeted me as I left the office this evening, looking across their lawn towards the gazebo.

This is the Grünbaum–Rigby 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.

Regular polygon surfaces:
Ian Alevy answers Problem 72 of The Open Problems Project ( 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, but Alevy's theorem doesn't apply, so we don't know whether all higher-genus regular-pentagon surfaces are formed that way.

A 3-regular matchstick graph of girth 5 consisting of 54 vertices (, 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:

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 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,

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.)

Show more

A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.

Use \( and \) for inline LaTeX, and \[ and \] for display mode.