Prime Knot: 7_5

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This text illustrates a prime knot 7_5, tied within a constant radius tube and tightened. The thin version features half-sized tubes to enhance visibility of crossings, while thick versions depict full-scale tubes which are easier to print with minimal support material. For more information on the 7_5 knot, visit its Knot Atlas page (http://katlas.math.toronto.edu/wiki/7_5). The knot's illustration is a product of RidgeRunner, a software freely available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. This program uses numerical algorithms to minimize the knot's length while maintaining a tube around it. The displayed shape is just one potential configuration for the knot, as varying functions can yield different models. To witness this particular prime knot tightening, refer to the movie at http://www.jasoncantarella.com/movs. For further details on tight knots and ropelength data, consult Wikipedia (http://en.wikipedia.org/wiki/Ropelength) and Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/) respectively.