Prime Knot: 6_1

thingiverse

The prime knot 6_1 is illustrated in a constant radius tube, tightened to its full potential. To observe its intricacies more clearly, a thinner version has been created by halving the tube's size. Alternatively, a thicker version exhibits the full scale of the tube. These versions are particularly beneficial during 3D printing as they require minimal support material. For comprehensive information about this knot, visit its page on Knot Atlas (http://katlas.math.toronto.edu/wiki/6_1). To learn more about tight knots and their significance, refer to Wikipedia's Ropelength entry (http://en.wikipedia.org/wiki/Ropelength). For ropelength data related to this specific knot, check Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). To visualize the process of the prime knot tightening, view the movie available at http://www.jasoncantarella.com/movs. This captivating animation was generated using RidgeRunner, a free software program created by Jason Cantarella, which can be downloaded from this link (http://www.jasoncantarella.com/wordpress/software/ridgerunner/). RidgeRunner utilizes a numerical algorithm to minimize the knot's length while maintaining a tube around it, although this is just one of numerous potential shapes for the topological knot. The program's output depends on the specific function being minimized.