Prime Knot: 3_1 (trefoil knot)

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The prime knot 3_1, also known as the trefoil or overhand knot, is displayed in a tube with constant radius and tightened in this rewritten text. Two versions are available - thin and thick. The thin version has a reduced tube size to enhance visibility of crossings. Printing these models requires less support material compared to full-scale tubes. For more information on the prime knot 3_1, visit its page on Knot Atlas (http://katlas.math.toronto.edu/wiki/3_1). The tightening concept can be explored further at Wikipedia (http://en.wikipedia.org/wiki/Ropelength). RidgeRunner, a software developed by the author, creates these knot shapes through minimizing knot length while preserving a tube around it. This numerical algorithm results in only one possible position for each topological knot. Download RidgeRunner at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. To view a movie of this prime knot tightening, check out http://www.jasoncantarella.com/movs.