Ivars Peterson's MathTrek
Crammed into a narrow wedge of land in downtown Princeton, N.J., an unusual but ephemeral park presents a quirky celebration of art, science, mathematics, architecture, and landscape design.
Named Quark Park, this Alice-in-Wonderlandish garden offers an enchanting visual and aural experience. Granite pillars ring with resonant tones. Crystal shafts sprout from sand, reaching for the sky. Glass bubbles float in a sparkling sea. Mirrored double helices flash fragments of light as they twirl in the breeze. An intricate, stainless-steel cage glints geometrically in brilliant sunlight.
The park was conceived, designed, and organized by architect Kevin Wilkes and colleagues Peter Soderman and Alan Goodheart. It temporarily fills a sliver of land that is to be redeveloped into housing, so the park is open to the public only through November.
The mathematical highlight is a stainless-steel sculpture by Marc Pelletier, honoring Princeton mathematician John H. Conway. The sculpture represents a three-dimensional shadow, or projection, of a famous, four-dimensional figure sometimes called the 120-cell, where each cell (or three-dimensional face) is a dodecahedron.
A regular dodecahedron has 30 edges and 12 faces, each of which is a regular pentagon. Its four-dimensional analoga polydodecahedroncontains 120 dodecahedra. Pelletier's sculpture embodies one possible, particularly symmetric projection of this four-dimensional object in three dimensions.
The sculpture, in which steel rods define the edges of the object's dodecahedra, features an undistorted dodecahedron at its center. This dodecahedron is surrounded by 12 others, which are only slightly distorted by foreshortening. Proceeding outward, the next layer has 20 dodecahedra, then 12 more that are considerably flattened by foreshortening. The final layer consists of 30 dodecahedra that are seen edge-on and so appear flat, delineating the sculpture's outer surface.
The original version of the 120-cell sculpture created by Pelletier is located at the Fields Institute in Toronto, where it honors geometer H.S.M. Coxeter, who died in 2003.
Another sculpture at Quark Park that has a mathematical element is the result of a collaboration between Princeton physicist Paul Steinhardt and sculptor Christoph Spath. Called "Forbidden Geometry," it is based on three-dimensional models of four different shapes that can be combined as building blocks to form so-called quasicrystals.
One of my favorite installations at Quark Park appears to have, at first glance, little to do with mathematics. Called "Motion in the Ocean," it consists of 1,200 hand-blown glass bubbles hanging from an overhead frame. The assemblage looks like a school of glistening fish, drifting underwater in a seaweedy nook.
Mechanical engineer Naomi Ehrich Leonard, who inspired the artwork, studies how animals use feedback to move as a cohesive whole, with the idea of applying similar principles to coordinate the movements of robots. The result may be a school of robotic underwater gliders. And there's certainly math in modeling the synchrony and interconnectedness required to get this to work.
It's a shame that this assemblage and all the other wonderful elements of Quark Park will soon disperse and disappear.
Additional information about Quark Park in Princeton, N.J., can be found at http://www.princetonoccasion.org/quarkpark/.
Peterson, I. 2000. Plato's molecule. MAA Online (Sept. 18).
______. 2000. Algebra, philosophy, and fun. MAA News Online (Jan. 17).
Phillips, T. 2006. The princess of Polytopia: Alicia Boole Stott and the 120-cell. American Mathematical Society (October). Available at http://www.ams.org/featurecolumn/archive/boole.html.
Comments are welcome. Please send messages to Ivars Peterson at firstname.lastname@example.org.