Prime Knot: 7_4

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This text demonstrates a prime knot 7_4, tied within a constant radius tube and tightened. The thin version reduces the tube's size to enhance visibility of crossings, while the thick version maintains full scale. Printing these is less demanding in terms of support material. For more information on this specific prime knot, visit its page at Knot Atlas (http://katlas.math.toronto.edu/wiki/7_4). To learn about tight knots, refer to Wikipedia (http://en.wikipedia.org/wiki/Ropelength), while ropelength data can be found at Jason Cantarella's website (http://www.jasoncantarella.com/wordpress/papers/). For a visual demonstration of this prime knot tightening, access the provided movie link (http://www.jasoncantarella.com/movs). This intricate model was created by the RidgeRunner software, freely accessible at http://www.jasoncantarella.com/wordpress/software/ridgerunner/. The program uses a numerical algorithm to minimize knot length while maintaining a tube around it. Although this is just one possible shape for the 7_4 prime knot, altering the function minimized would generate a different model.