Prime Link: 8_3_1

thingiverse

The prime link 8_3_1 is illustrated in two versions, with a constant radius tube that's tightened. The thin version has a reduced tube size to enhance visibility of crossings, while the thick version appears at full scale. These models are easier to print with minimal support material. To learn more about this prime link, visit its page on Knot Atlas (http://katlas.math.toronto.edu/L8a18). For information on tight knots and ropelength data, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength) and Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/) respectively. Additionally, a movie of this prime link tightening can be found on Jason Cantarella's website (http://www.jasoncantarella.com/movs). This knot shape is a product of RidgeRunner software, which is available for free download at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. RidgeRunner uses a numerical algorithm to minimize the length of a knot while maintaining a tube around it, resulting in varying shapes based on different functions being minimized.