October 26, 2014

11:21 PM | Another 5-permutohedron
I've been playing with the Cayley graphs of the symmetric group again, after accidentally running across the Wikipedia article on the icositruncated dodecadodecahedron and thinking "oh yeah, that's the polyhedron that geometrically represents the Cayley graph generated by a transposition and a 4-cycle".Only, it's not. That was a different star polyhedron. So is the icositruncated dodecadodecahedron also a permutohedron? And if so, what are the generators of the corresponding Cayley graph?To […]

October 15, 2014

8:30 PM | Linkage
Why academic writing stinks or, keep it simple (G+)Sad news of the death of Ferran Hurtado (G+)A visual compendium of glowing creatures, scientific illustration by Eleanor Lutz (G+)Women in computer science get tenure at significantly lower rates than men even after normalizing for research productivity (G+)Tietze's graph, Wikipedia article expanded with a new illustration of why it has the name it has: it was an earlier counterexample in the theory of coloring graphs on non-orientable surfaces […]

October 14, 2014

11:17 PM | 2-site Voronoi triangle centers
The idea of a 2-site Voronoi diagram was pioneered by Barequet, Dickerson, and Drysdale in a WADS 1999 paper later published in Discrete Applied Math. 2002. The basic idea is that you have a function d(p,q;x) that tells you the distance from an unordered pair of sites {p,q} to another point x in the plane; given a collection of sites, you want to divide the plane up into regions so that the region containing a point x tells you which pair of sites is closest to x (or in some […]

October 09, 2014

12:57 AM | Forced creases in Miura folding
I've posted before about the Miura fold, a subdivision of a sheet of paper into paralellograms that gives a nice smooth motion from a compact folded state (in which the parallelograms are all folded on top of each other) to an unfolded state in which the paper is nearly flat. But this pattern can have defects that interfere with its folding pattern, in which small subunits of the pattern fold the wrong way: they still have the same creases but some of them are backwards. My latest arXiv […]

October 01, 2014

3:09 AM | Linkage for the end of September
Algomation animated algorithms (G+)Rush hour video, or, what our robot-driven future will be like (G+)The Washington Post rants about those evil student pirates, but neglects to mention the free alternatives (G+)A song video about knots, from the low-dimensional topology blog (G+)Fun hex grid facts, via MF (G+)SODA 2015 accepted papers (G+)KaTeX, a lobotomized but fast web math renderer (G+)Against laptops in lectures, via MF (G+)David Wade’s ‘Fantastic Geometry’ – The […]
5 Results