English

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

History and Overview 2023-10-04 v2 Differential Geometry

Abstract

Minimal surfaces can be though as a mathematical generalisation of surfaces formed by soap films. We consider Bour's minimal surfaces Bm\mathcal{B}_m that are intrinsically surfaces of revolution. We show how to generate crochet patterns for Bm\mathcal{B}_m surfaces using basic trigonometric identities to calculate required arc lengths. Three special cases of Bm\mathcal{B}_m surfaces are considered in more detail, namely Enneper's, Richmond's, and Bour's B3\mathcal{B}_3 surfaces, and we provide exact crochet instructions for the classical Enneper's surface.

Cite

@article{arxiv.2306.15378,
  title  = {Crocheting Bour's $\mathcal{B}_m$ minimal surfaces},
  author = {Hanne Kekkonen},
  journal= {arXiv preprint arXiv:2306.15378},
  year   = {2023}
}
R2 v1 2026-06-28T11:15:34.077Z