Roice's G+ Posts

This video goes through the proof using the free group F_2 sitting inside SO(3), without mentioning it as such. I hadn't heard of Ian Stewart's Hyperwebster before, but it's a really nice lead-in. Jump to  8:12 if you're happy with Cantor's diagonal argument and Hilbert's hotel and want to skip definitions of countably/uncountably infinite. #scienceeveryday   #mathematics   https://youtu.be/s86-Z-CbaHA

I enjoyed this talk, especially the latter part.  It was interesting to hear about all the thought that has gone into hyperbolic manifolds with infinite volume and "exotic manifolds" that are "geometrically infinite" (a distinction I do not yet understand).  Thanks for your post Refurio Anachro! Originally shared by Refurio Anachro The Royal Institution was founded in 1799, and since the beginning it has been supporting public engagement with science. In their gorgeous premises they've been hosting the "Friday Evening Discourses" pop science lectures since 1825, nowadays recorded on video for you to watch. Those are for everyone and it's not unusual for them to have many kids in the audience. A recent one is "Topology, Geometry and Life in Three Dimensions" given by Caroline Series . She is striving hard to explain William Thurston 's geometrization conjecture for the uninitiated, and it's the first recording where i saw the au...

Originally shared by American Mathematical Society This image by Roice Nelson shows the boundary of the {7,3,3} honeycomb featured previously on the Visual Insight blog. The black circles are holes, not contained in the boundary of the {7,3,3} honeycomb. There are infinitely many holes, and the actual boundary, shown in white, is a fractal with area zero. Read more from John Baez: http://blogs.ams.org/visualinsight/2014/08/14/733-honeycomb-meets-plane-at-infinity/ #images #mathimagery #fractals #mathematics   http://blogs.ams.org/visualinsight/2014/08/14/733-honeycomb-meets-plane-at-infinity

Originally shared by Erno Rubik A 5-dimensional Analogue of the Rubik's Cube You can now try to solve a 5-dimensional Rubik's Cube. How many permutations of the 3x3 cube in 5-dimensions?  Approx. 7.0 x 10^560 Good luck. Visit here to download the program and learn more: http://www.gravitation3d.com/magiccube5d/index.html #mathematics   #geometry   #rubikscube

Feels good to see a past project pop up unexpectedly.  The 5D Rubik's cube was born in 2006 in the 4D_Cubing yahoo group, though it was conceived much earlier!  See this 1982 paper by Kamack and Keane: http://helm.lu/cube/tesseract.pdf Here's the 4D_Cubing page: http://groups.yahoo.com/neo/groups/4D_Cubing/info And you can browse the messages from March to May 2006, when all the excitement was happening: http://groups.yahoo.com/neo/groups/4D_Cubing/conversations/messages?messageStartId=215&archiveSearch=true This is the first time I've seen the new yahoo groups interface, so hopefully those links will work. Originally shared by annarita ruberto MagicCube5D In the spirit of taking things too far, here is a fully functional 5-dimensional analogue of Rubik's cube. The 3D cube has 43252003274489856000 permutations. Go here to learn more and  download the program : http://www.gravitation3d.com/magiccube5d/index.html Here you find  Erno Rubik, the inventor of  fa...