Intersecting Helices

Paul Gailiunas
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 381–384


In two dimensions a sequence of equally spaced parallel lines will intersect with another such sequence set at some angle to form a regular tiling of rhombi. If the lines are replaced by sine curves there are many more possibilities, depending on the relative phases of the curves. In three dimensions sets of parallel lines will intersect only in particular cases, since usually lines from different sets will be skew. A helix is a natural three-dimensional analogue of a sine curve, and again arrays of helices will intersect only in particular cases. Such configurations are so intricate visually that even small pieces of the infinite structure provide interesting sculptural forms.