# Isoperimetric problem

1. Jan 13, 2012

### HACR

1. The problem statement, all variables and given/known data
The isoperimetric problem is of the finding the object that has the largest area with the equal amount of perimeters; however, how does the integral constrained by the arc length get maximized? http://mathworld.wolfram.com/IsoperimetricProblem.html

2. Relevant equations

3. The attempt at a solution
...finding a point at which the integral is like finding the max and min of a function of two variables...

2. Jan 13, 2012

### LCKurtz

The general subject is Calculus of Variations. One place to read about it is here:

It says the shortest path is the straight line; however, the brachistochrone problem proves that it is actually a curved line on which a stone could accelerate more. OK, brachistochrone problem is discussed. But why is on page 1163, the Euler Lagrangian equal to $$-\frac{u"}{(1+(u')^2)^{\frac{3}{2}}}$$? I got -u"+(u')^{2}u" for numerator.