Marc Chamberland

Myra Steele Professor of Natural Sciences and Mathematics
Grinnell College
Grinnell, Iowa, USA

I have long been enchanted by the aesthetic side of mathematics. Most people view mathematics as a collection of tools and procedures and get mired in the mechanics. Mathematical art communicates the essential beauty found in mathematics. As G. H. Hardy (1877-1947) wrote, "The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics."

Borromean Five
Borromean Five
18cm x 18 cm x 4 cm
High Performance Composite made with a 3D printer

The traditional "Borromean rings" is a set of three intertwined space curves. Versions of the rings have been used as religious symbols (in churches, for example, to represent the trinity) and more recently as company logos. From an "aerial" perspective, each curve is above one of the other curves and below the other curve. This comparison of curves is similar to the strategies used in the game rock-paper-scissors: each strategy beats another strategy (example: rock beats scissors) and is beaten by another strategy (example: rock is beaten by paper).

The art piece depicts a set of five identical, intertwined space curves where each curve beats two other curves and is beaten by the remaining two. Topologically, this set of closed space curves is the unique link with this comparison property. The link has been rendered so that, viewed from above, each space curve is a circle. This link compares with the game rock-paper-scissors-lizard-Spock.