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Spring 2002 Some Bonnesen-Style Triangle Inequalities
Stanley Rabinowitz
Missouri J. Math. Sci. 14(2): 75-87 (Spring 2002). DOI: 10.35834/2002/1402075

Abstract

Some Bonnesen-style isoperimetric inequalities for triangles in the plane are presented. For example, it is shown that $L^2-12 \sqrt 3 A \geq 35.098 \,\,\, r(R-2r)$ for triangles with perimeter $L$, area $A$, inradius $r$, and circumradius $R$. Equality holds when and only when either the triangle is equilateral or the triangle is similar to the isosceles triangle with sides 1, 1, and $\lambda$ where $\lambda\approx 1.23628634$ is the largest root of the equation $31x^3-28x^2-16x+4=0$.

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Stanley Rabinowitz. "Some Bonnesen-Style Triangle Inequalities." Missouri J. Math. Sci. 14 (2) 75 - 87, Spring 2002. https://doi.org/10.35834/2002/1402075

Information

Published: Spring 2002
First available in Project Euclid: 4 October 2019

zbMATH: 1033.52008
MathSciNet: MR1907844
Digital Object Identifier: 10.35834/2002/1402075

Rights: Copyright © 2002 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.14 • No. 2 • Spring 2002
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