most citedPolygonal approximation and energy of smooth knots

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2 papers

math.GT2005

Polygonal knot space near ropelength-minimized knots

Kenneth C. Millett, Michael Piatek, Eric J. Rawdon

For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r<R(K) de…

math.GT2003★ 1 cited

Polygonal approximation and energy of smooth knots

Eric J. Rawdon, Jonathan K. Simon

We establish a fundamental connection between smooth and polygonal knot energies, showing that the Minimum Distance Energy for polygons inscribed in a smooth knot converges to the…