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Showing posts from December, 2017

Math Outreach

Math Outreach

Perhaps the best part of an up and down 2017... Sarah and I established an endowment that will fund a math outreach program at The University of Texas at Austin. We were recently profiled in Texas Leader magazine about it.

http://texasleadermagazine.utexas.edu/prime-exponent/
http://texasleadermagazine.utexas.edu/prime-exponent/

Single cell of a {3,7,3}

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Single cell of a {3,7,3}

Now that I'm set up to render 2-dimensional faces of a honeycomb in my 3D prints, here's another. I'm really loving the translucency of the thin walls. In proper lighting, edges in this model have enough extra thickness to stand out in darkened contrast, which looks especially cool. Check that out in the second picture below.

This self-dual honeycomb has been in my feed before because Henry Segerman and I did an art piece based on it for Bridges a few years back. We called it "Hyperbolic Catacombs" and you can read a little more about the honeycomb at its gallery page.

http://gallery.bridgesmathart.org/exhibitions/2015-bridges-conference/roice3

Because I included only one cell, this model is less than a third the price of the {7,3,3} model I posted recently. You can order it from Shapeways at the following link (again, with no markup), and there is even still time to get it for Christmas!

http://shpws.me/Pg8e

Teaser: I'm about to orde…

Physical 4-dimensional Puzzle!?!

Physical 4-dimensional Puzzle!?!

This is a new and very special puzzle just shared with the world from one of my creative heroes, Melinda Green. It's a bit magical that it can even exist, and a number of mathematical properties had to be just so for it to be possible.

The program MagicCube4D has long allowed playing the 4-dimensional analogue of a 2x2x2 Rubik's "Pocket" cube on the computer. With this combinatorially equivalent physical puzzle, you can play the 2x2x2x2 in your hands. It goes to show how keeping hope alive for something over a long period of time, and considering the possibility of it in many different ways, can pay off.

The way I like to think of the puzzle is to consider the 4-dimensional hypercube projected to the 3-sphere. Then regard the 3-sphere topologically as two balls glued along their boundary. Both of the 2x2x2 blocks in the physical puzzle are one of those balls, representing a hemisphere of the 3-sphere and of the higher dimensional …

It feels silly to reshare John’s posts because anyone following me is surely following him too, but I can’t help...

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It feels silly to reshare John’s posts because anyone following me is surely following him too, but I can’t help myself when he posts about things I’ve worked on!

Originally shared by John Baez

The beauty of hyperbolic heptagons

Check out Roice Nelson's new picture! This picture lives in hyperbolic space, which been squashed down to a ball. The 'dents' are hyperbolic planes tiled by regular heptagons, each subdivided into 7 red and 7 blue triangles.

These triangles don't look like they have the same size - but in 3d hyperbolic space they do! The problem is that we've squashed hyperbolic space down to a ball. It's impossible to fit hyperbolic space in ordinary Euclidean space without doing violence to it.

Hyperbolic space has a group of symmetries called the Lorentz group. This is famous in special relativity: it's the group containing rotations and also Lorentz transformations.

The Lorentz group has symmetries that can map any of the red or blue triang…