• May 15, 2019

  Linkage

  • El poema de los números primos ($\mathbb{M}$). Exhibit of the mathematically-inspired artworks of Esther Ferrer, at Tabakalera in San Sebastián, Spain.
• May 2, 2019

  Playing with model trains and calling it graph theory

  You’ve probably played with model trains, for instance with something like the Brio set shown below.¹ And if you’ve built a layout with a model train set, you may well have wondered: is it possible for my train to use all the parts of my track?

  1. Searching on tineye finds that this image was on Amazon in 2008. Presumably it was supplied to them by Brio? ↩

• Apr 30, 2019

  Linkage

  • Good article, terrible headline ($\mathbb{M}$). Bill Gasarch rants about several recent instances of clickbaity, inaccurate, and overhyped media coverage of theoretical computer science topics. I suspect the answer to his question “is it just our field?” is no.
• Apr 23, 2019

  Euler characteristics of non-manifold polycubes

  From a $2\times 2$ block of cubes, remove two non-adjacent and non-opposite cubes. The resulting polycube has a boundary that is not a manifold: between the two removed cubes, there is an edge shared by four squares, but a two-dimensional manifold can only have two faces per edge. Nevertheless, we can compute its Euler characteristic as the number of vertices ($25$) minus the number of edges ($47$) plus the number of square faces ($24$). $25-47+24=2$, the same number we would expect for the Euler characteristic of a topological sphere! What does it mean?

• Apr 15, 2019

  Linkage

  • “You know how the \hat command in LaTeΧ puts a caret above a letter? … Well I was thinking it would be funny if someone made a package that made the \hat command put a picture of an actual hat on the symbol instead?” And then Matthew Scroggs and Adam Townsend went ahead and did it ($\mathbb{M}$).
• Apr 14, 2019

  Monochromatic grids in colored grids

  Color the points of an $n\times n$ grid with two colors. How big a monochromatic grid-like subset can you find? By “grid-like” I mean that it should be possible to place equally many horizontal and vertical lines, partitioning the plane into $k\times k$ cells each of which contains a single point.

• Apr 11, 2019

  Coloring kinggraphs

  Draw a collection of quadrilaterals in the plane, meeting edge to edge, so that they don’t surround any open space (the region they cover is a topological disk) and every vertex interior to the disk touches at least four quadrilaterals. Is it always possible to color the corners of the quadrilaterals with four colors so that all four colors appear in each quadrilateral?

• Apr 7, 2019

  Photos from Barbados

  I spent this year’s spring break at Erik Demaine’s annual computational geometry workshop in Barbados again. A few photos of workshop participants:

• Mar 31, 2019

  Linkage

  • A 3-regular matchstick graph of girth 5 consisting of 54 vertices, Mike Winkler, Peter Dinkelacker, and Stefan Vogel ($\mathbb{M}$). 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 made another drawing of the same graph in a different style:
• Mar 15, 2019

  Linkage

  It’s the last day of classes for the winter quarter here at UCI, and a good time for some spring cleaning of old bookmarked links. Probably also a good time for a reminder that Google+ is shutting down in two weeks so if, like me, you still have links to it then you don’t have long to replace them with archived copies before it gets significantly more difficult.

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