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The Existence of a Triangle

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Recent Advances in Geometric Inequalities

Part of the book series: Mathematics and Its Applications ((MAEE,volume 28))

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Abstract

This Chapter is concerned with existence of a triangle satisfying prescribed conditions. Of course, it is well-known that a, b, c are sides of a triangle if and only if a, b, c ≥ 0, b+c ≥ a, c+a ≥ b, a+b ≥ c. If we wanted to rule out degenerate triangles, we would have to omit the equality signs.

Chapter XIII also contains many criteria for the existence of a triangle and of some other figures in E2 and E3

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Authors and Affiliations

  1. University of Belgrade, Yugoslavia

    D. S. Mitrinović

  2. University of Zagreb, Yugoslavia

    J. E. Pečarić & V. Volenec

Authors
  1. D. S. Mitrinović
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  2. J. E. Pečarić
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  3. V. Volenec
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© 1989 Springer Science+Business Media Dordrecht

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Mitrinović, D.S., Pečarić, J.E., Volenec, V. (1989). The Existence of a Triangle. In: Recent Advances in Geometric Inequalities. Mathematics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7842-4_1

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  • DOI: https://doi.org/10.1007/978-94-015-7842-4_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8442-2

  • Online ISBN: 978-94-015-7842-4

  • eBook Packages: Springer Book Archive

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