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Linkage

May 31, 2017

  • Packing Petersen graphs into \(K_{10}\), Peter Cameron. Three don’t fit exactly, but you can cover \(K_{10}\) with four Petersens so that the extra edges form another cubic graph.

  • Animation of Miquel’s five circles theorem (G+). Given a cycle of five circles with crossing points of consecutive circles all on a sixth circle, the other five crossing points form the crossings of a pentagram with points on the red circles. A dual version (every pentagram has six associated circles) also seems to be true.

  • MathML is a failed web standard, Peter Krautzberger (G+). “It doesn’t matter whether or not MathML is a good XML language … It’s clearly a success in the XML publishing world, serving an important role in standards such as JATS and BITS. The problem is: MathML has failed on the web.”

  • Tories use child porn and terrorism as an excuse to censor political speech on the British internet. “[Tech companies] would be forced to help controversial government schemes like its Prevent strategy, by promoting counter-extremist narratives. … The Conservatives will also seek to regulate the kind of news that is posted online … If elected, Theresa May will ‘take steps to protect the reliability and objectivity of information that is essential to our democracy.’”

  • Frechet distances between one-dimensional trajectories (G+). An amusingly acted and not-too-technical video, featuring Maarten Löffler as a crazed papercrafter.

  • Exhaustive search of convex pentagons which tile the plane by Michaël Rao. Rao claims to have a computational proof that the 15 known types of monohedral convex pentagon tiles are the only ones possible.

  • The new Cambridge North train station is decorated with cellular automata (G+). But despite wanting to honor Conway they chose Wolfram’s Rule 30 instead of Conway’s Game of Life.

  • Punctured surface, Alison Grace Martin (G+). A kagome basketweave pattern with judiciously placed heptagons in place of the usual hexagons allows its paper strips to follow approximate geodesics on a nontrivial topological surface.

  • Physical stop-motion animation of the Dirac belt trick, Gerard Westendorp (G+). Westendorp writes “I find it fascinating that you can rotate something by an infinite angle, without net twisting its connection to solid earth.”

  • Fermat Point by Suman Vaze, Chalkdust magazine (G+). Triangle centers as fine art.

  • Jeff Erickson shares two recent preprints on breakthroughs relating to his research (G+): “Hanani–Tutte for approximating maps of graphs” by Rado Fulek and Jan Kynčl, and “Near-optimal linear decision trees for \(k\)-SUM and related problems” by Kane, Lovett, and Moran.

  • Artistic expressions of math over seven centuries (G+). Selections from the Department of Drawings and Prints, Metropolitan Museum of Art.

  • All possible pythagorean triples, visualized, 3Blue1Brown (G+). The formula for generating all primitive pythagorean triples becomes a lot more intuitive when you visualize it in terms of complex numbers and their transformations.

  • Paywall Watch, a new site that tracks commercial journal publishers who charge for papers that were supposed to be open access. Also see their interview on RetractionWatch and profile on TheScientist.

  • David Eppstein

Geometry, graphs, algorithms, and more