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Convex Hulls Of Simple Space Curves

Published online by Cambridge University Press:  20 November 2018

Douglas Derry
Douglas Derry*
Affiliation:
University of British Columbia
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The convex hull of an arbitrary set M in real Euclidean n-space is known to consist of all the points within the r-simplexes with r + 1 vertices from M, r ≤ n. This note shows that if M is specialized to be a curve An of real order n, then its convex hull consists of all the points within the r-simplexes with r + 1 vertices on An, n = 2r + 1 or n = 2r.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 383 - 388
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Egerváry, E., On the smallest cover of a simple arc of space curve. Publ. Math. Debrecen 1 (1949), 65–70.Google Scholar
2. Karlin, S. and Shapley, L. S., Geometry of moment spaces. Mem. Amer. Math. Soc. 12 (1953).Google Scholar