28 citations · 187 across the 25 of their papers we have counts for
3 papers · 1 filter
The Expected Total Curvature of Random Polygons
Jason Cantarella, Alexander Y Grosberg, Robert B. Kusner +1
We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference be…
Symmetric Criticality for Tight Knots
Jason Cantarella, Jennifer Ellis, Joseph H. G. Fu +1
We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configu…
Probability Theory of Random Polygons from the Quaternionic Viewpoint
Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler
We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Knutson and Hausmann using the Hopf map on quaternions, from the comp…