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Inequalities for Simplexes in En (n ≥ 2)

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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

Let V be the volume and r inradius of a given n-simplex A = A1A2 ... An+1 in n-dimensional Euclidean space En (n ≥ 2). For any i ∈ {1, 2,.., n} let Fi be the (n−1)-dimensional content of (n−1)-simplex A i = A1 ... Ai−1Ai+1 ... An+1, let hi = AiA′i be the altitude of A from vertex Ai, i.e. the distance from Ai to the hyperplane ai = A1 ... Ai−1Ai+1 ... An+1′ and let ρi be the radius of i-th escribed hypersphere of A. Let

$$ F = \sum\limits_{i = 1}^{n + 1} {{F_i}} $$
(1)

be the ‘total area’ of A. For every i ∈ {1, 2,..., n + 1} we have

$$ {h_i} = \frac{{nV}}{{{F_i}}}{\text{ (i = 1,2,}} \ldots {\text{,n + 1)}} $$
(2)

.

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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

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  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). Inequalities for Simplexes in En (n ≥ 2). In: Recent Advances in Geometric Inequalities. Mathematics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7842-4_18

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  • DOI: https://doi.org/10.1007/978-94-015-7842-4_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8442-2

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