Linkage

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 counterextremist 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 onedimensional trajectories (G+). An amusingly acted and nottootechnical 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 stopmotion 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 “Nearoptimal 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.