**Statement of The Inequality**

Let *K* and *L* be two *n*-dimensional convex bodies in *n*-dimensional Euclidean space **R***n*. Define a quantity *V*_{1}(*K*, *L*) by

where *V* denotes the *n*-dimensional Lebesgue measure and + denotes the Minkowski sum. Then

with equality if and only if *K* and *L* are homothetic, i.e. are equal up to translation and dilation.

Read more about this topic: Minkowski's First Inequality For Convex Bodies

### Other articles related to "statement of the inequality, inequality":

**Statement of The Inequality**

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**inequality**holds Equivalently, taking ...

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—John Dewey (1859–1952)

“It is commonplace that a problem stated is well on its way to solution, for *statement of* the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.”

—John Dewey (1859–1952)

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