# Difference between revisions of "Isoperimetric Inequalities"

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===Isoperimetric Inequality=== | ===Isoperimetric Inequality=== | ||

− | If a figure in the plane has area <math>A</math> and perimeter <math>P</math> then <math>\frac{4\pi A}{P^2} | + | If a figure in the plane has area <math>A</math> and perimeter <math>P</math> then <math>\frac{4\pi A}{P^2} \leq 1</math>. This means that given a perimeter <math>P</math> for a plane figure, the circle has the largest area. Conversely, of all plane figures with area <math>A</math>, the circle has the least perimeter. |

==See also== | ==See also== |

## Revision as of 22:46, 21 June 2006

### Isoperimetric Inequality

If a figure in the plane has area and perimeter then . This means that given a perimeter for a plane figure, the circle has the largest area. Conversely, of all plane figures with area , the circle has the least perimeter.