Prime Knot: 7_1

thingiverse

This text illustrates a prime knot 7_1, showcased in thin and thick versions tied within tubes of constant radius. The thin version has reduced tube size for enhanced visibility of crossings, while thicker ones exhibit full-scale tubes, easier to print with minimal support material. For more information on the prime knot 7_1, visit its Knot Atlas page at http://katlas.math.toronto.edu/wiki/7_1. Understand tight knots better through Wikipedia's ropelength info (http://en.wikipedia.org/wiki/Ropelength), and for ropelength data, explore Jason Cantarella's site (http://www.jasoncantarella.com/wordpress/papers/). To visualize this prime knot tightening, watch the movie at http://www.jasoncantarella.com/movs. This model was created using RidgeRunner, a freely accessible software available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. RidgeRunner uses numerical algorithms to minimize knot length while maintaining a tube around the knot. Different functional minimizations yield distinct shapes for this topological knot.