Abstract
One of the most striking projective theorems concerning the twisted cubic is that any three osculating planes of the cubic meet in a point coplanar with their points of osculation. Thus the twisted cubic sets up, in this manner, a null system in space. Let us more generally define an n-curve as a curve such that: (A) the points of osculation of all osculating planes to the curve through a point are coplanar with the point, (B) the osculating planes of a set of coplanar points of the curve are copunctual at a point on their plane. An n-curve, then, also sets up a null system in space, and the twisted cubic is but a particular n-curve.
An earlier version of this paper, motivated by work done in differential geometry by Dirk Struik, appeared in National Mathematics Magazine 19 (1944), 1–7. Permission has been granted to use this revised version.
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© 1974 D. Reidel Publishing Company, Dordrecht-Holland
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Eves, H. (1974). Skew Curves Setting Up a Null System in Space. In: Cohen, R.S., Stachel, J.J., Wartofsky, M.W. (eds) For Dirk Struik. Boston Studies in the Philosophy of Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2115-9_6
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DOI: https://doi.org/10.1007/978-94-010-2115-9_6
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