Roice's G+ Posts

Wacky Conformal Transformation I was trying to conformally stretch out the band model to more of the euclidean plane, and ran across this strange thing. I don't understand all the features, but it's pretty.  It was generated by first applying the band model transformation to the disk, rotating that 90 degrees and scaling, then applying the band model transformation again. Anybody know of a conformal transformation of the Poincaré disk that maps to a large area of the euclidean plane while keeping hyperbolic tiles approximately the same size?  I suspect it may not be possible, since the amount of material one needs to fit in grows exponentially.  If it is possible, I bet such a thing would need to be undulating, with some areas of smaller tiles and other areas with larger tiles. Reference Vladimir Bulatov's work, "Conformal Models of Hyperbolic Geometry", bulatov.org/math/1001/

A new kind of book with tons of fascinating geometry. Illustrations are available as models for 3D printing. Originally shared by Henry Segerman My book is now available for preorder! https://jhupbooks.press.jhu.edu/content/visualizing-mathematics-3d-printing

{7,3} Surfboard Finale The mathematical surfboard is finished! It turned out perfectly, and I'm so happy with the result. Thanks Sarah Nemec-Nelson for a wonderful 10th anniversary present. I'll get some pictures or video of it in action up at some point :D For more, see {7,3} Surfboard Part 1: plus.google.com/+RoiceNelson/posts/iSmtVvE7xTV And {7,3} Surfboard Part Deux: plus.google.com/+RoiceNelson/posts/FL96TdMRvCE

Henry Segerman appears on Numberphile! Originally shared by Numberphile Extra footage: https://youtu.be/pCCtcqyazOE https://www.youtube.com/watch?v=uAnCL3vhVIs&feature=autoshare

This is exciting! Gil's post doesn't actually say what the densest sphere packings in dimensions 8 and 24 are, but if you click through to the paper abstracts, they are the packings based on the E8 lattice and the Leech lattice. I wonder if this was the result mathematicians expected? Thanks David Eppstein for the reshare. Originally shared by Gil Kalai https://gilkalai.wordpress.com/2016/03/23/a-breakthrough-by-maryna-viazovska-lead-to-the-long-awaited-solutions-for-the-densest-packing-problem-in-dimensions-8-and-24/ https://gilkalai.wordpress.com/2016/03/23/a-breakthrough-by-maryna-viazovska-lead-to-the-long-awaited-solutions-for-the-densest-packing-problem-in-dimensions-8-and-24

It's been an exciting (and somewhat sleep deprived) week watching these games. Melinda Green has some positive thoughts on the outcome of the match. Originally shared by Melinda Green Here is the board position and Lee Sedol at the moment when he resigned the match to AlphaGo. You'll be hearing a lot about this stunning achievement in the news with some people gushing about the technology and others wailing about the blow to humanity's collective ego. I'd like to offer another perspective on what I think it all means. Yes, it's the end of an era, but it's also the beginning of an amazing new one. But not the age of SkyNet and killer robots, though certainly some of that is coming, and definitely not the end of human dominance and evolution. I like to think of our artificially intelligent creations as our silicon children. And just like all good parents hope for their children to do better than they did, I feel very proud at this moment and want to celebrate that...

These are beautiful.  This particular folding reminded me of a snub {7,3} hyperbolic tiling, like here: www.plunk.org/~hatch/HyperbolicTesselations/3_7_snub_512x512.gif It's very different though (the triangles don't have the same edge length as the heptagons, for one), so now I'm wondering if there is a hyperbolic tiling like this. Thanks Jacob Dix for the reshare. Originally shared by Jenny Winder http://illusion.scene360.com/art/91610/robby-kraft-origami/