Isoperimetry

In mathematics, the isoperimetric inequality is a geometric inequality involving the surface area of a set and its volume. In ${\displaystyle n}$-dimensional space ${\displaystyle \mathbb {R} ^{n}}$ the inequality lower bounds the surface area ${\displaystyle \mathrm {surf} (S)}$ of a set ${\displaystyle S\subset \mathbb {R} ^{n}}$ by its volume ${\displaystyle \mathrm {vol} (S)}$,

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