Prime Knot: 8_21

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The prime knot 8_21 is illustrated by tightening it within a tube of constant radius in two versions - thin and thick. The thin version has reduced tube size to aid visibility, while the thick one appears at full scale, requiring less support material during printing. To comprehend more about this prime knot, refer to its page on Knot Atlas (http://katlas.math.toronto.edu/wiki/8_21). The model is designed by my open-source program RidgeRunner (http://www.jasoncantarella.com/wordpress/software/ridgerunner/) that minimizes the knot length while maintaining a tube around it. Different function optimizations yield distinct shapes for this topological knot. A movie showcases this prime knot tightening at http://www.jasoncantarella.com/movs. For further insights on tight knots, visit Wikipedia (http://en.wikipedia.org/wiki/Ropelength), and for ropelength data, explore Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/).