Crocheting Bour's ${\mathcal{B}}_m$ minimal surfaces

Abstract

Minimal surfaces can be though as a mathematical generalisation of surfaces formed by soap films. We consider Bour's minimal surfaces ${\mathcal{B}}_m$ that are intrinsically surfaces of revolution. We show how to generate crochet patterns for ${\mathcal{B}}_m$ surfaces using basic trigonometric identities to calculate required arc lengths. Three special cases of ${\mathcal{B}}_m$ surfaces are considered in more detail, namely Enneper's, Richmond's, and Bour's ${\mathcal{B}}_3$ surfaces, and we provide exact crochet instructions for the classical Enneper's surface.