Victor Groth: Rational Tangles

Abstract

In this workshop the goal is to introduce a class of tangles of ropes called rational tangles. We start by introducing them by actually tangling ropes, using two simple actions on them. Showing, with examples, that we can untangle any tangle with the same two moves. I'll let you work on optimizing solutions to tangles (with real ropes!). 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 commutating way. We further explore this bijection by introducing addition and multiplication of tangles. This is directly based on a workshop I do with gymnasium kids at Vetenskapens Hus.