Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Université Pierre et Marie Curie
Paris, France

tel: +33 1 44 27 72 61
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e-mail: sebastien.neukirch (-atat-) upmc.fr

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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.

DOI: 10.1285/i15900932v32n1p87

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