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Helices through 3 or 4 points?

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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Publication date:
2011-01-01
URN:
uuid:53c050cc-0746-4710-a4d5-b11833f319e6
Local pid:
oai:eprints.maths.ox.ac.uk:1445

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