Roice's G+ Posts

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

It feels great contributing to Visual Insight images! Originally shared by John Baez {7,3,3} meets the plane at infinity Maryam Mirzakhani won the Fields medal largely for her work on hyperbolic geometry.  The hyperbolic plane is something we can all enjoy: it's not flat, but curved like a saddle, and triangles have angles that add up to less than 180 degrees.  We can draw it crushed down to a disk, as in this picture by Roice Nelson.  All the light blue circles should really be the same size - but the ones near the edge have been squashed. Instead of learning Euclidean geometry in school, you could have learned hyperbolic geometry - it's almost the same, with some big differences.  The main thing is that the parallel postulate is false in hyperbolic geometry: there are many ways to draw a line through a point parallel to another line!  This is how Lobachevsky  discovered hyperbolic geometry in 1823: by seeing what would happen if you changed the rules t...

Originally shared by David Eppstein http://www.boredpanda.com/iran-mosque-photography-mohammad-domiri/

It was awesome to see an image from a past project used by my favorite astrophysics blogger.  Thanks Brian Koberlein for using a Gravitation3D picture and referring to the program! Make your own solar systems and set them in motion here...   www.gravitation3d.com Originally shared by Brian Koberlein Accentuate the Negative There’s news on the web that cosmologists have proven the existence of negative mass. The news is based upon an article that recently appeared on the preprint arxiv, and has not yet been peer reviewed. The article in no way proves the existence of negative mass, but rather demonstrates the theoretical possibility of a form of negative mass within general relativity. In other words, it is an interesting “what if” paper rather than applied astrophysics. Usually when we talk about the mass of an object we think of it as a basic property of an object. Mass is always positive in quantity, so negative mass must be the same thing but opposite. But in fact ther...

This is great, and captures a pretty common state of affairs for me :) Originally shared by Calvin and Hobbes

(2 3 7) Triangles and Klein's Quartic My new favorite t-shirt arrived in the mail today, designed by Henry Segerman. This design and many others with mathematical themes are available at Henry's website. http://www.segerman.org/tshirts.html I used the "create" version of the shop to slightly alter the size and color. http://math-art-create.spreadshirt.com/us/US/Shop/ So what is this design? In short, it is a tiling of (2 3 7) triangles.  The (2 3 7) designates a Schwarz triangle.  It means the 3 angles of each triangle are π/2, π/3, and π/7.  Schwarz triangles can tile the sphere, Euclidean plane, or hyperbolic plane depending on the choice of the 3 angles.  (2 3 7) triangles tile the hyperbolic plane, and Henry has drawn these triangles in the Poincare disk model, cutting off the model at some radius from the origin.  My G+ banner is a similar representation of (2 3 7) triangles tiling the disk, but with a different choice of cutoff and as a 3D printed model. ...

I recommend watching the talks too! Originally shared by Henry Segerman This is a walkthrough of Saul Schleimer's and my art exhibition at the Simons Center for Geometry and Physics at Stony Brook.  The posters are available at https://www.dropbox.com/sh/ycugkbxmii1k9zf/AACdkp0C5LV8FvBBw0-GiMAga The catalog is available at http://www.math.okstate.edu/~segerman/exhibitions/illustrating_geometry_catalog.pdf We gave two talks, which can be viewed at "Illustrating Geometry" exhibition at SCGP, Artist's talk: "Sculpture in four-dimensions" and "Illustrating Geometry" exhibition: Artist's talk by Saul Schleimer: "Minimal and Seifert Surfaces" Many thanks to Maria Froehlich, Tim Young, Katherine Schwarting and Margaret Schedel for all of their help, and to George Hart for helping us with dyeing some of the sculptures. Thanks also to the Museum of Mathematics and Tony Phillips for the loan of their artworks for the show. http://www.youtube.c...