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Parameterized Knots

Lee Stemkoski (Adelphi Univ.)


We discuss two families of parameterized knots (polynomial and trigonometric) and include an interactive gallery of selected knots and their equations.  We survey results related to parameterizations and suggest avenues for further investigation.  Finally, we include an applet that graphs three-dimensional parametric curves to aid the interested reader in exploring additional parameterizations.


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This article uses LiveGraphics3D, a Java applet which displays three-dimensional figures as generated by Mathematica. Any figure displayed with LiveGraphics3D can be rotated by clicking and dragging the mouse on the image.

Lee Stemkoski (Adelphi Univ.), "Parameterized Knots," Convergence (May 2011), DOI:10.4169/loci003596