## Saturday, March 19, 2016

### Lux: a new and exciting mathematical construction kit

I'm a big fan of mathematically inspired construction kits, like Zometools, and found out about a new one that looks really awesome. It's called Lux, and here's the amazon description:
With Lux's patent-pending snap and lock hinge, builders are now freer than ever before to make structures which curve, bend, and move. Not only do our squares make circles and spheres, but they model machines, biological organisms, mathematical relationships, and enable a user to construct whatever architecture they want. Put the creative power of nature in your hands.
I found out about Lux through a facebook post by its creator Mike Acerra:

Not to get too hyperbolic about this , but yes, Lux has been proven to be exactly that. Oklahoma State Math professor...
Posted by Mike Acerra on Friday, March 18, 2016

Here's the rest of the text of the post, as you can't seem to click and see more'':
Henry Segerman, assistant professor in the Department of Mathematics at Oklahoma State University, does research in 3-dimensional geometry and topology, particularly involving ideal triangulations. His interest is in mathematical and typographical art of various kinds and dimensions.
In December 2015, Segerman discovered that because Lux builds using the rule of five squares around every vertex, (normally a square tile would fit four around a corner and make a “flat plane”) it can model hyperbolic space.
The significance of this is that when we tile the hyperbolic plane, we have vastly more freedom than we do in the limited Euclidean world. We can tile it with equilateral triangles, quadrilaterals, pentagons, hexagons, and so on. Not only that, we can do it infinitely many ways with each of those shapes. Angles are much more restricted in Euclidean space than in hyperbolic space.
Hyperbolic geometry has been used to better understand Einstein’s special theory of relativity because Einstein used the geodesic or elliptical geometry of Bernhard Riemann, which was also used in the invention of Buckminster Fuller’s famed “Geodesic Domes”.
And that's totally groovy.
I don't own any of these blocks (yet), but they look super interesting! Let me know what you think if you've gotten a chance to play with them!