Abstract
Starting from the triangle inequality, we will discuss a series of shape optimization problems using elementary geometry and ultimately derive the classical isoperimetric inequality in the plane.
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A Sitaram, The isoperi-metric problem, Resonance, Vol.2, No.9, pp.65–68, 1997.
S Kesavan, The isoperimetric inequality, Resonance, Vol.7, No.9, pp.8–18, 2002.
R Courant and H Robbins, What is Mathematics?, Second Edition (revised by Ian Stewart), Oxford University Press, 1996.
S Hildebrandt and A Tromba, The Parsimonious Universe: Shape and Form in the Natural World, Copernicus Series, Springer, 1996.
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S Kesavan works at the Institute for Mathematical Sciences, Chennai. His area of interest is partial differential equations with specialization in elliptic problems connected to homogenization, control theory and isoperimetric inequalities. He has authored four books covering topics in functional analysis and its applications to partial differential equations.
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Kesavan, S. From the triangle inequality to the isoperimetric inequality. Reson 19, 135–148 (2014). https://doi.org/10.1007/s12045-014-0017-y
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DOI: https://doi.org/10.1007/s12045-014-0017-y