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Centre National de la Recherche Scientifique
Université Pierre et Marie Curie
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Helices through 3 or 4 points?
A. Goriely, S. Neukirch, and A. Hausrath
Note di Matematica, vol. 32 #1 (2012) pp 87-103
Abstract : How many points in space are needed to define a circular helix? We show here that given 3 distinct points in space there exist continuous families of helices passing through these points. Given 4 generic distinct points there is no helix. However, a discrete family of helices through 3 points can be specified if an additional property of the helix is prescribed. In particular, the case where the helical radius is specified is studied in detail.
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