Prime Knot: 5_1

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This model demonstrates the prime knot 5_1, also known as the (5,2) torus knot, tied within a tube of constant radius and pulled tight. In the slim version, the tube is halved to show crossings more clearly; the thick version represents it at full scale, requiring less support material. For additional information about this specific prime knot, visit its page on Knot Atlas (http://katlas.math.toronto.edu/wiki/5_1). To learn more about tight knots, explore Wikipedia's ropelength entry (http://en.wikipedia.org/wiki/Ropelength), and for ropelength data, access Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). Witness the knot tightening process in a movie available at http://www.jasoncantarella.com/movs. This intricate design is generated by RidgeRunner, a free-to-use software program developed by Jason Cantarella (http://www.jasoncantarella.com/wordpress/software/ridgerunner/). RidgeRunner utilizes numerical algorithms to minimize the knot's length while maintaining a tube around it, creating unique shapes for each topological knot depending on the function being minimized.