What's the name given to the ratio $P^2/A$ for a closed figure in the Euclidean plane?

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Let $\mathscr{F}$ be the set of all plane, closed Euclidean figures having positive perimeter, and let $\sim$ be the similarity relation on $\mathscr{F}$.

Then, for any equivalence class $\widetilde{F} \in \mathscr{F}/ \sim$, the ratio $P^2/A$, where $P$ stands for the perimeter and $A$ for the area, is invariant over $\widetilde{F}$.

Does this ratio $P^2/A$ have a standard name?


1For example, when $\widetilde{F}$ is the class of all squares this ratio is $16$, and when $\widetilde{F}$ is the class of all circles, it is $4 \pi$. The isoperimetric inequality theorem asserts that (1) the latter value is in fact a lower bound for the ratio, as $\widetilde{F}$ ranges over $\mathscr{F}/\sim$; and (2) it is not attained by any other equivalence class in $\mathscr{F}/\sim$. On the other hand, it's not hard to see that this ratio has no upper bound.

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The Encyclopedia of Math calls it isoperimetric ratio, and Google finds quite a few articles using that phrase for it.