Invited Speaker
Teresita Ramirez-Rosas
Upper Bound for the Ropelength of a Trefoil Knot
The ropelength of a knot K is defined as the shortest length of unit radius rope needed to tie the knot K. The principal goal is to find an upper bound for its ropelength. In 2005, Justyna Baranska, Piotr Pieranski and Eric Rawdon found a polygonal knot with 1920 edges and unit normal injectivity radius that has length 32.7431. This is the last upper bound for a trefoil knot. We improved this upper bound by finding a trefoil knot with normal injectivity radius one and length 32.6039. Since the current lower bound is 32.31, we know that the ropelength of a trefoil knot lie between 31.32 and 32.6039. The construction suggests that the ropelength is likely to be very close to our upper bound.