This paper provides an explanation and proof of the Isoperimetric Inequality of simple closed curves in the set of pairs of real numbers. We will show that among all simple closed curves bounding a given area, the curve with the shortest length is a circle. Likewise, among all simple closed curves of a given length, the curve that bounds the greatest area is a circle.
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McAuliffe, Aidan P.
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Christina Tonnesen-Friedman
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Jeffrey Hatley