Difference between revisions of "Isoperimetric Inequalities"
(Changed < to \leq) |
|||
| Line 1: | Line 1: | ||
===Isoperimetric Inequality=== | ===Isoperimetric Inequality=== | ||
| − | If a figure in | + | If a figure in a 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== | ||
| Line 8: | Line 8: | ||
* [[Area]] | * [[Area]] | ||
* [[Perimeter]] | * [[Perimeter]] | ||
| + | |||
| + | [[Category:Theorems]] | ||
Revision as of 13:45, 8 November 2007
Isoperimetric Inequality
If a figure in a 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.
