Taffy, Trees, and Tangles

TL;DR

This paper explores the connections between taffy pulling machines, Calkin-Wilf trees, and Conway's rational tangles, establishing new geometric and combinatorial relationships among these objects.

Contribution

It introduces a taffy analogue for rational tangles and provides a direct geometric link between tangles and taffy pulls, unifying these concepts.

Findings

Established a taffy analogue for rational tangles

Connected rational tangles with taffy pulls geometrically

Unified combinatorial and geometric perspectives on tangles

Abstract

We study the relationship between three combinatorial objects -- a taffy pulling machine, the Calkin-Wilf tree of all fractions, and Conway's rational tangles. After introducing these objects, we develop a taffy analogue for Conway's characterization of rational tangles, and we give a direct geometric connection between rational tangles and taffy pulls.