 ##  [Isoperimetric Inequality](/isoperimetric-inequality) 

  ##  [Isoperimetric Inequality](https://natural.quantumdictionary.io/isoperimetric-inequality-0) 

  
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**Natural &amp; Formal Sciences Dictionary**

 
Definition

A family of geometric inequalities that bound the boundary measure (perimeter, surface area) of a region from below in terms of its volume, asserting that among sets with fixed volume the ball (sphere) minimizes the boundary measure.

 
 ##  [Isoperimetric Inequality](https://puremath.quantumdictionary.io/isoperimetric-inequality-1) 

  
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- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

The statement in planar Euclidean geometry that for any bounded region with perimeter P and area A we have 4πA ≤ P², with equality exactly for round disks; equivalently, among plane regions with given perimeter the circle encloses the maximal area.