Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1975-0357701-9
MathSciNet review: 0357701
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A15

Retrieve articles in all journals with MSC: 26A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0357701-9
Keywords: Horizontal chord, change of sign, zero
Article copyright: © Copyright 1975 American Mathematical Society