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A generalisation to several dimensions of the Neuberg-Pedoe inequality, with applications

  • Yang Lu (a1), Zhang Jing-Zhong (a1) and B.H. Neumann
Abstract

A well-known inequality relating the areas and squares of the sides of two triangles is generalised to higher-dimensional euclidean spaces. Extension of the results to non-euclidean spaces is also considered.

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References
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[1]Alexander, Ralph, “Two notes on metric geometry”, Proc. Amer. Math. Soc. 64 (1977), 317320.
[2]Beckenbach, Edwin F. and Bellman, Richard, Inequalities (Ergebnisse der Mathematik land ihrer Grenzgebiete, N.F. 30. Springer-Verlag, Berlin, Göttingen, Heidelberg, 1961).
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[11]Pedoe, Daniel, “Thinking geometrically”, Amer. Math. Monthly 77 (1970), 711721.
[12]Pedoe, Dan, “Inside-outside: the Neuberg-Pedoe inequality”, Univ. Beograd. Publ. Elektrotechn. Fak. Ser. Mat. Fiz. 544–576 (1976), 9597.
[13]Lu, Yang and Zhong, Zhang Jing, “A class of geometric inequalities on finite points”, Acta Math. Sinica 23 (1980), 740749 (Chinese).
[14]Lu, Yang and Zhong, Zhang Jing, “A high-dimensional extension of the Neuberg-Pedoe inequality and its application”, Acta Math. Sinica 24 (1981), 401408 (Chinese).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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