Skip to main content

In praise of inequalities

  • Chapter
Proofs from THE BOOK

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Alzer: A proof of the arithmetic mean-geometric mean inequality, Amer. Math. Monthly 103 (1996), 585.

    Article  MathSciNet  MATH  Google Scholar 

  2. P. S. Bullen, D. S. Mitrinovics & P. M. Vasić: Means and their Inequalities, Reidel, Dordrecht 1988.

    MATH  Google Scholar 

  3. P. Erdős & T. Grünwald: On polynomials with only real roots, Annals Math. 40 (1939), 537-548.

    Article  Google Scholar 

  4. G. H. Hardy, J. E. Littlewood & G. Pólya: Inequalities, Cambridge University Press, Cambridge 1952.

    MATH  Google Scholar 

  5. W. Mantel: Problem 28, Wiskundige Opgaven 10 (1906), 60-61.

    Google Scholar 

  6. G. Pólya: Review of [3], Mathematical Reviews 1 (1940), 1.

    Google Scholar 

  7. G. Pólya & G. Szegő: Problems and Theorems in Analysis, Vol. I, Springer-Verlag, Berlin Heidelberg New York 1972/78; Reprint 1998.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Aigner, M., Ziegler, G.M. (2010). In praise of inequalities. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00856-6_18

Download citation

Publish with us

Policies and ethics