# A Tale of Two Integrals

Year of Award: 2000

Publication Information: The American Mathematical Monthly, vol. 106, 1999, pp. 227-240

Summary: This paper presents several approaches to a simple-looking combinatorial-analysis problem with the aim of showing how different ideas can lead to a solution.  The analysis version of the problem can be stated as follows: If $$f$$ and $$g$$ are functions each having integral over $$[0,1]$$ equal to $$1$$, then there is some subinterval of $$[0,1]$$ over which each integral is equal to $$1/2$$.

About the Author: (from The American Mathematical Monthly vol. 106 (1999))

Vilmos Totik was born in 1954 in Hungary. He is a professor at the Bolyai Institute, Szeged, Hungary and also at the University of South Florida, Tampa. He is a member of the Hungarian Academy of Sciences. He has (co)authored four research monographs: Moduli of Smoothness, General Orthogonal Polynomials, Logarithmic Potentials with External Fields, and  Weighted Approximation with Varying Weights. His loves are his family (Veronika, Orsolya, Zoltan), his profession (approximation theory, orthogonal polynomials, potential theory), sports (soccer, tennis, table tennis), and any other normal activities (gardening, carpentry,…).

Author (old format):
Vilmos Totik
Author(s):
Vilmos Totik
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Publication Date:
Tuesday, September 23, 2008
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Summary:

This paper presents several approaches to a simple-looking combinatorial-analysis problem with the aim of showing how different ideas can lead to a solution. The analysis version of the problem can be stated as follows: If $$f$$ and $$g$$ are functions each having integral over $$[0,1]$$ equal to $$1$$, then there is some subinterval of $$[0,1]$$ over which each integral is equal to $$1/2$$.