Editing Perimeter (section)

== Isoperimetry ==
{{Further|Isoperimetric inequality}}

The isoperimetric problem is to determine a figure with the largest area, amongst those having a given perimeter. The solution is intuitive; it is the [[circle]]. In particular, this can be used to explain why drops of fat on a [[broth]] surface are circular.

This problem may seem simple, but its mathematical proof requires some sophisticated theorems. The isoperimetric problem is sometimes simplified by restricting the type of figures to be used. In particular, to find the [[quadrilateral]], or the triangle, or another particular figure, with the largest area amongst those with the same shape having a given perimeter. The solution to the quadrilateral isoperimetric problem is the [[square]], and the solution to the triangle problem is the [[equilateral triangle]]. In general, the polygon with {{math|''n''}} sides having the largest area and a given perimeter is the [[regular polygon]], which is closer to being a circle than is any irregular polygon with the same number of sides.