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Recent Advances in Geometric Inequalities pp 443–462Cite as

Particular Inequalities in Plane Geometry

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

Abstract

A classical isoperimetric inequality states that, for a simple closed curve C of length L in the plane, the area F enclosed by C satisfies

EquationSource % MathType!MTEF!2!1!+- % feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaCa % aaleqabaGaaGOmaaaakiabgkHiTiaaisdacqaHapaCcaWGgbGaeyyz % ImRaaGimaiaac6caaaa!3F1E!]]</EquationSource><EquationSource Format="TEX"><![CDATA[$$ {L^2} - 4\pi F \geqslant 0. $$
(1)

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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). Particular Inequalities in Plane Geometry. In: Recent Advances in Geometric Inequalities. Mathematics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7842-4_17

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  • DOI: https://doi.org/10.1007/978-94-015-7842-4_17

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