Laura Taalman, Stephen Lucas, and Abigail Eget

Professor of Mathematics
James Madison University
Harrisonburg, VA, USA

Laura Taalman and Stephen Lucas are professors of mathematics at James Madison University, where they mentor undergraduate research projects that live at the intersection of mathematics, art, design, and experimental computation. Abigail Eget is a mathematics major at James Madison University who has been exploring tritangentless knot conformations and 3D design techniques.

Rolling Knots
Rolling Knots
8 x 40 x 12 cm
3D printed nylon knots and wooden board

Tritangentless knots have a curious and beautiful property: when realized as physical 3D printed models, they roll. Some tritangentless parameterizations roll more easily and freely than others, depending on the vertical and horizontal movement of their centers of mass. We have optimized a family of tritangentless trefoils to obtain the best rolling knots in terms of vertical center of mass variation. In this interactive work, people are invited to roll 3D printed models of these optimized rolling knots along a board and physically experience their horizontal center of mass variations as the models "rock and roll" down an inclined board.