Category Archives: Mathematical Art

Stars of the Mind’s Sky

I just submitted some art for exhibition at Bridges 2013, the world’s largest mathematical art conference.  I’m extremely hopeful that it will be accepted.  I actually submitted art for exhibition at the Joint Mathematics Meetings, but it was denied, I think, because I hadn’t figured out how to get the right image size and resolution.  Whoops.  Anyhow, I’m proud of what I put together, and I wanted to share it with you here, so I’ve pasted the art, description, and my artist’s statement below.  (And yes.  I will sell you a print if you’d like.)

* * *

My earliest love of mathematics came when I realized its utility in creating beautiful things. As a third grader (and ever since), I spent countless afternoons drawing stars and patterned shapes with a protractor or compass. In my work as a teacher I get to share that beauty in creation with my students. In my art I sometimes try to illuminate the complex structure and interconnectedness of simple, patterned objects. I’m compelled to understand complete spaces of related works and how my choices as an artist locate me within that space.

Stars of the Mind's Sky22.75 in x 22.75 in digital print 2012

Stars of the Mind’s Sky
22.75 in x 22.75 in
digital print

Stars of the Mind’s Sky is the title of a series of works exploring the space of regular star polygons. Here we see 300 stars “in orbit” along concentric circles. The number of points on a star increases with the radius, and stars of a given number of points are spaced evenly along their circle according to “density,” or the “jump number” used in generating them. Algebraically, these represent the subgroups and cosets generated by elements of a cyclic group. They have been colored on a gradient to indicate the number of cosets; a red star signifies a generating element. As a consequence of these structural choices, we may observe congruent stars with increasingly many cosets, shifting their way to blue along central rays through any red star.

The Meta-meta-node

We made this as part of our MArTH Madness mathematical art festival at Saint Ann’s. Dozens of students and teachers worked together to build 60 metanodes out of Zome. Then about 15 people worked together to piece them together into an even larger rhombicosidodecahedron. It’s a Zome ball made out of zome balls made out of zome balls!!! It stands about 5.5 feet tall, and its now resting safely in our basement art gallery.


A Zome node made from Zome nodes made from Zome nodes!

A student's picture, found on instagram

A student’s picture, found on instagram

To actually construct it, we built the top first, and then lifted it to build beneath so that the weight would hold the struts together during construction. In the end we held the dome up and slid the bottom underneath it. Amazingly, it held together in front of a big, cheering crowd.

I love MArTH Madness.  We’ve been thinking about this model for a while, and to see it actually finished feels amazing.  As one student put it, “It’s like we wanted to do it, and then we did it, and now it’s done.”  I love that.

Update: Justin posted a fantastic video showing the different node sizes.  Enjoy!