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

Hans Rademacher, I. J. Schoenberg

Type: Article

Publication Date: 1950-01-01

Citations: 26

DOI: https://doi.org/10.4153/cjm-1950-022-8

Abstract

Professor Dresden called to our attention the following theorem : If S 1 , S 2 , … , S m 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.

Locations

Canadian Journal of Mathematics - View - PDF

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+ PDF Chat	The dimension of intersections of convex sets	1962	Branko Grünbaum
+ PDF Chat	Partitions of mass-distributions and of convex bodies by hyperplanes	1960	Branko Grünbaum
+	Helly-type theorems for pseudoline arrangements in P2	1982	Jacob E. Goodman Richard Pollack
+	Best Uniform Approximation of Complex-Valued Functions by Generalized Polynomials Having Restricted Ranges	1999	G. S. Smirnov Roman G. Smirnov
+ PDF Chat	Contraction and Expansion of Convex Sets	2009	Michael Langberg Leonard J. Schulman
+ PDF Chat	Theorems on the existence of separating surfaces	1991	Michael E. Houle
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+	Metric methods in linear inequalities	1948	Leonard M. Blumenthal
+	Mengen konvexer K�rper, die einen gemeinsamen Punkt enthalten	1921	Johann Radon