Folding of quadrilaterals, zigzags, and Arnold-Liouville integrability

TL;DR

This paper explores the mathematical properties of quadrilateral folding and zigzag patterns, connecting classical geometric porisms with modern integrability theory, specifically Arnold-Liouville integrability.

Contribution

It introduces a novel perspective by linking geometric folding problems to Arnold-Liouville integrability, unifying classical and modern mathematical concepts.

Findings

Establishes a connection between quadrilateral folding and integrability.

Provides a new framework for understanding geometric porisms.

Bridges classical geometry with modern dynamical systems theory.

Abstract

We put Darboux's porism on folding of quadrilaterals, as well as closely related Bottema's zigzag porism, in the context of Arnold-Liouville integrability.