Victor Groth: Rational Tangles

Abstract

In this workshop/talk my goal is to introduce you to a class of tangles of ropes called rational tangles. We start by introducing them by actually tangling ropes, using two simple actions on them. We will show, by examples, that we can untangle any tangle with the same two moves. I'll let you work on optimizing solutions to tangles. For the second half I will connect them back to math, showing that there is a bijection between these tangles and the rational numbers that maps these 2 actions to functions, in a commuting way. We further explore this bijection by introducing addition and multiplication of tangles. This is directly based on a workshop I do with high-school kids at Vetenskapens Hus.