isoperimetric problem

The simplest of the isoperimetric problemsMathworldPlanetmath is the following:

One must set an arc with a given length l from a given point P of the plane to another given point Q such that the arc together with the line segment PQ encloses the greatest area possible.

This task is solved in the entry example of calculus of variationsMathworldPlanetmath.

More generally, isoperimetric problem may determining such an arc c between the given points P and Q that it gives for the integral

PQf(x,y,y)𝑑s (1)

an extremum and that gives for another integral

PQg(x,y,y)𝑑s (2)

a given value l, as both integrals are taken along c.  Here, f and g are given functions.

The constraint (2) can be omitted by using the function f-λg instead of f in (1) similarly as in the mentionned example.

Title isoperimetric problem
Canonical name IsoperimetricProblem
Date of creation 2013-03-22 19:12:01
Last modified on 2013-03-22 19:12:01
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 9
Author pahio (2872)
Entry type Definition
Classification msc 47A60
Classification msc 49K22
Related topic IsoperimetricInequality
Related topic LagrangeMultiplier