Prime Link: 8_2_8

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This text depicts a prime link 8_2_8, exhibited in both thin and thick versions within a tube of constant radius. The slim variant allows better visibility of crossings, while the full-scale version necessitates less support material during printing. For more information about this specific prime knot, refer to its page on Knot Atlas (http://katlas.math.toronto.edu/L8a9). This illustration was generated using RidgeRunner, a free software that employs numerical algorithms to minimize the length of a knot while maintaining a tube around it. The program is available for download at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. It's crucial to note that this particular shape represents just one possible configuration for the topological knot; alternative minimization functions could result in different model forms. To gain further insights into tight knots, consult Wikipedia (http://en.wikipedia.org/wiki/Ropelength). For ropelength data, explore Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). To witness a movie of this prime link tightening, visit http://www.jasoncantarella.com/movs.