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In praise of inequalities

  • Martin Aigner
  • Günter M. Ziegler

Abstract

Analysis abounds with inequalities, as witnessed for example by the famous book “Inequalities” by Hardy, Littlewood and Pólya. Let us single out two of the most basic inequalities with two applications each, and let us listen in to George Pólya, who was himself a champion of the Book Proof, about what he considers the most appropriate proofs.

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References

  1. [1]
    H. Alzer: A proof of the arithmetic mean-geometric mean inequality, Amer. Math. Monthly 103 (1996), 585.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    P. S. Bullen, D. S. Mitrinovics & P. M. Vasic: Means and their Inequalities, Reidel, Dordrecht 1988.zbMATHGoogle Scholar
  3. [3]
    P. Erdös & T. Grünwald: On polynomials with only real roots, Annals Math. 40 (1939), 537–548.CrossRefGoogle Scholar
  4. [4]
    G. H. Hardy, J. E. Littlewood & G. Pólya: Inequalities, Cambridge University Press, Cambridge 1952.zbMATHGoogle Scholar
  5. [5]
    W. Mantel: Problem 28, Wiskundige Opgaven 10 (1906), 60–61.Google Scholar
  6. [6]
    G. Pőlya: Review of [3], Mathematical Reviews 1 (1940), 1.Google Scholar
  7. [7]
    G. Pőlya & G. Szegő: Problems and Theorems in Analysis, Vol. I, Springer-Verlag, Berlin Heidelberg New York 1972/1978; Reprint 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Institut für Mathematik, MA 6-2Technische Universität BerlinBerlinGermany

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