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

See also

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