Prime Knot: 4_1 (figure-8 knot)
thingiverse
The prime knot 4_1, also known as the figure-8 knot, is depicted in this model. It's tied within a tube of constant radius and pulled tight. A thinner version displays crossings more clearly, while the thicker version appears at full scale. These are easier to print with less support material. For further information on 4_1, refer to its page on Knot Atlas (http://katlas.math.toronto.edu/wiki/4_1). To learn about tight knots and ropelength, consult Wikipedia (http://en.wikipedia.org/wiki/Ropelength). Rope length data can be found at Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). You can also watch a movie of this prime knot tightening on Jason Cantarella's site (http://www.jasoncantarella.com/movs). This model is generated by RidgeRunner, a free software available at http://www.jasoncantarella.com/wordpress/software/ridgerunner. It minimizes knot length while maintaining a tube around the knot using numerical algorithms. Different functions can yield distinct shapes for this topological knot.
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