
Linkage
For the new year, I’ve decided to try to get back into taking photos more frequently, and to make it loweroverhead I’m making individual Mastodon posts for some of them rather than writing a longer blog post for every batch of photos. So that’s why you see a couple of those images inline here.

Linkage for the end of the year
 LaTeX, the game (, G+, via). It should be an even higher level to get the commutative diagram to format in Wikipedia’s lobotomized version of LaTeX.

Motorcycle graphs and the eventual fate of sparse Life
The motorcycle graph is a geometric structure devised by Jeff Erickson as a simplified model for the behavior of straight skeletons, motivated by the light cycle game in the movie Tron. Its initial data consists of a set of points in the plane (the motorcycles), each with an initial velocity. The motorcycles leave a trail behind them as they move, and a motorcycle crashes (stopping the growth of its trail) when it hits the trail of another motorcycle.

Circles crossing at equal angles
Let , , , and be four circles, with pairs , , , and crossing at equal angles (and no crossings among the other two pairs). Then it turns out that the two curvy quadrilaterals forming the inside and outside boundaries of the union of disks each have a circle through their four vertices:

Linkage
This is my penultimate link roundup before I give up on Google+, rather than holding out for its rapidlyapproaching demise.

Generalposition hypercube projections
I recently posted about finding solutions to the nothreeinline problem of finding large generalposition subsets of grids, by using the probabilistic method or by throwing an integer linear program solver at the problem. Another potential method for finding solutions involves finding large generalposition subsets in higher dimensions, where it’s easier (there’s more room to move the points out of the way of each other), and then projecting back down while being careful not to introduce any new collinearities.

TriplyHamiltonian edge colorings
Mark Jason Dominus recently made a blog post about the interesting observation that the regular dodecahedron can have its edges properly colored with three colors so that every two colors form a Hamiltonian cycle. Here’s another view of the same dodecahedral coloring:

Linkage
In which I discover kramdown’s inability to pass raw verticalbar characters to MathJax… (workaround: use
\vert
) 
Linkage
I’m gradually shifting weight to my Mastodon account and away from my doomed G+, but I hope to stick with both through the end of the year to provide a gradual transition. Today’s step: the Mastodon links go first.

Gurobi versus the nothreeinline problem
For the nothreeinline problem, it has been known since the 1990s that grids with have sets of points with no three in line. Those results, by Achim Flammenkamp, were based on custom search software and a lot of compute time. I was curious to see how far one could get with moremodern but generic optimization codes, so this weekend I ran a little experiment.
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