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Helly's Theorems on Convex Domains and Tchebycheff's Approximation Problem

Published online by Cambridge University Press:  20 November 2018

Hans Rademacher  and
I. J. Schoenberg
Hans Rademacher
Affiliation:
The University of Pennsylvania
I. J. Schoenberg
Affiliation:
The University of Pennsylvania
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Professor Dresden called to our attention the following theorem :

If S1, S2,… , Sm are m line segments parallel to the y-axis, all of equal lengths, whose projections on the x-axis are equally spaced, and if we assume that a straight line can be made to intersect every set of three among these segments, then there exists a straight line intersecting all the segments.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 245 - 256
Copyright
Copyright © Canadian Mathematical Society 1950

References

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