From Chain-link Fence to Space-Spanning Mathematical Structures

Tom Verhoeff and Koos Verhoeff
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 73–80 Regular Papers


Chain-link fence is constructed from intertwined zigzag wires. Such a fence is basically a two-dimensional structure, which can be extended infinitely in two directions. We describe various ways in which zigzags can be intertwined to produce potentially infinite three-dimensional structures. Next, we generalize the zigzags to helices, and explore their possibilities to span space. These zigzags and helices can be constructed from beams using miter joints. Appropriate choices for the cross section and the kind of miter joint results in artistically appealing sculptures. Several designs were constructed in wood. Along the way, we discovered a nice invariance theorem for helices.