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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Horizontal chords of the graph of a continuous function


Author: Uwe Herzberg
Journal: Proc. Amer. Math. Soc. 49 (1975), 179-184
MSC: Primary 26A15
MathSciNet review: 0357701
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Abstract: The continuous function $ f$, defined on $ [a,b]$, changing sign exactly $ n$ times on $ (a,b)$, and $ f(a) = f(b) = 0$, has horizontal chords of every length $ h < H$ with endpoints in $ (a,b)$. We determine the largest such $ H$ as a function of $ n$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0357701-9
PII: S 0002-9939(1975)0357701-9
Keywords: Horizontal chord, change of sign, zero
Article copyright: © Copyright 1975 American Mathematical Society