Composite Knot: 3_1 # 3_1 (square and granny versions)

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This is a model of the composite knot 31#_3_1, or the composition of two overhand or trefoil knots. Since the trefoil knot comes in left and right-handed versions, there are two versions of this composite knot: the square knot 3_1 # 3_1_m, where a left-handed and right-handed trefoil are spliced together, and the granny knot 3_1 # 3_1 where two trefoils of the same handedness are spliced together. 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 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 composite 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 one possible position for this (topological) knot; minimizing a function other than length would give you a different shape for the model.