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math.GT2003
Total Curvature and Packing of Knots
Gregory Buck, Jonathan Simon
We establish a new fundamental relationship between total curvature of knots and crossing number. If K is a smooth knot in 3-space, R the cross-section radius of a uniform tube nei…
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…