Prime Knot: 8_9

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This is a model of the prime knot 8_9. It is tied in a tube of constant radius, and pulled tight. In the thin version, the tube has been reduced to half-size in order to help you see the crossings. In the thick version, the tube appears at full scale. These are easier to print without as much support material. For more information about this prime knot, look at its page in the Knot Atlas http://katlas.math.toronto.edu/wiki/8_9. For more information about tight knots, see http://en.wikipedia.org/wiki/Ropelength. For ropelength data, see http://www.jasoncantarella.com/wordpress/papers/. To see a movie of this prime knot tightening, visit http://www.jasoncantarella.com/movs. Instructions This knot shaped is created by my knot tightening program RidgeRunner, which is freely available at http://www.jasoncantarella.com/wordpress/software/ridgerunner/ RidgeRunner uses a numerical algorithm to minimize the length of a knot while preserving a tube around the knot. This is only possible position for this (topological) knot; minimizing a function other than length would give you a different shape for the model.