Isoperimetric Inequalities

Revision as of 13:07, 11 June 2008 by Temperal (talk | contribs) (add)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Isoperimetric Inequalities are inequalities concerning the area of a figure with a given perimeter. They were worked on extensively by Lagrange.

If a figure in a 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.

Note that due to this inequality, it is impossible to have a figure with infinite volume yet finite surface area.

See also

Invalid username
Login to AoPS