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Continuous Families of Curves

Published online by Cambridge University Press:  20 November 2018

Branko Grünbaum
Branko Grünbaum*
Affiliation:
Hebrew University, Jerusalem and Michigan State University
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The present paper is an attempt to find the unifying principle of results obtained by different authors and dealing—in the original papers—with areabisectors, chords, or diameters of planar convex sets, with outwardly simple planar line families, and with chords determined by a fixed-point free involution on a circle. The proofs in the general setting seem to be simpler and are certainly more perspicuous than many of the original ones. The tools required do not transcend simple continuity arguments and the Jordan curve theorem. The author is indebted to the referee for several helpful remarks.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 529 - 537
Copyright
Copyright © Canadian Mathematical Society 1966

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