Play, drawing, toys and sculpture have always been core to my own mathematical understanding. I have been illustrating mathematics as long as I have been practicing mathematics, which is to say, as long as I can remember, trying to render the abstract tangible. Conversely, many of my research interests are anchored in concrete hands-on exploration.
Sharing this perspective is central to my work as a teacher, artist, and mathematician, through fun hands-on classroom activities for kids, mathematical outreach, my academic research, group sculpture builds, or my work at the National Museum of Mathematics.
symmetries of the four dimensional sphere.
Artworks
Dodecafoam blocks
30.0 x 30.0 x 30.0 cm
PLA plastic
2024
The Dodecafoam blocks show a packing of space with dodecahedra, all scaled by powers of the golden ratio $\phi$ to each other. The blocks are derived from the “stellations” of the dodecahedron, the division of space by its facial planes. Each shape of block may be subdivided into smaller copies of shapes, recursively defining this structure. With simple matching rules, these blocks become aperiodic tiles, able to be formed into tilings of space, but only non-periodic ones.
From drawings using a photocopier thirty years ago, through sets of cardboard models and computer renderings, it is only now that home 3D printers are fine enough that I can finally feel the texture in my fingers and see this structure live.
Four orthogonal Hopf fibrations
30.0 x 30.0 x 30.0 cm
nylon tubing, pla plastic
2022
The tubing in this sculpture all lies along circles (or lines, circles of infinite radius). In fact, we can fill all of space continuously with each color of circle — these are each stereographic projections of a Hopf fibration, a division of the hypersphere into circles. The red, green, and blue fibrations are oppositely handed from the yellow one, and they all meet at right angles. In the hypersphere, these circles have symmetry denoted [[get back to you]] in Conway's notation --- this sculpture is one of a series illustrating many of these symmetries.
[[the piece looks a lot better in 3D!]]
