Isoperimetric Inequalities: Difference between revisions
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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}{ | If a figure in the plane has area <math>A</math> and perimeter <math>P</math> then <math>\frac{4\pi A}{P^2} < 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 21:33, 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.
