Geometric Inequalities

  • Albert W. Marshall
  • Ingram Olkin
  • Barry C. Arnold
Part of the Springer Series in Statistics book series (SSS)


Although the triangle has a limited number of parameters (sides, angles, altitudes, etc.), the range of inequalities among these entities is surprisingly large. Bottema, Djordjević, Janić, Mitrinović, and Vasić (1969), in their book Geometric Inequalities, have collected approx- imately 400 inequalities for the triangle. It is shown in this chapter 5 that majorization provides a unified approach to obtaining many known geometric inequalities. This unification also has the advantage of suggesting new inequalities.


Great Area Isoperimetric Inequality Isosceles Triangle Middle Term Plane Figure 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Albert W. Marshall
    • 1
    • 2
  • Ingram Olkin
    • 3
  • Barry C. Arnold
    • 4
  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Lummi IslandUSA
  3. 3.Department of StatisticsStanford UniversityStanfordUSA
  4. 4.Department of StatisticsUniversity of CaliforniaRiversideUSA

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