# isoperimetric inequality

Last Updated on September 24, 2022 by amin

Contents

## What is green and Stokes Theorem?

Green and Stokes’ Theorems are generalizations of the Fundamental Theorem of Calculus, letting us relate double integrals over 2 dimensional regions to single integrals over their boundary; as you study this section, it’s very important to try to keep this idea in mind.

## What is the plane closed curve of fixed perimeter and maximum area?

The plane curve of fixed perimeter and maximum area is CIRCLE.

## Which of the following curves gives maximum area subject to the fixed perimeter?

in Civil Engineering. Maths keeps one mentally active. A circle encloses maximum area for a given perimeter followed by a square. In Euclidean geometry, for a plane figure, it’s a circle.

## Who proved the Isoperimetric inequality?

There are, in fact, two ways to measure the spherical area enclosed by a simple closed curve, but the inequality is symmetric with the respect to taking the complement. This inequality was discovered by Paul Lvy (1919) who also extended it to higher dimensions and general surfaces.

## What is Isoperimetric problem?

isoperimetric problem, in mathematics, the determination of the shape of the closed plane curve having a given length and enclosing the maximum area. (In the absence of any restriction on shape, the curve is a circle.)

## What is Green theorem in calculus?

In vector calculus, Green’s theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C. It is the two-dimensional special case of Stokes’ theorem.

## Which of the curve gives maximum area subject to the fixed perimeter?

A circle gives the maximum area for a given perimeter. So the triangle that gives the maximum area for a given perimeter is an equilateral triangle.

## Why do we use Stokes Theorem?

Stokes’ theorem provides a relationship between line integrals and surface integrals. Based on our convenience, one can compute one integral in terms of the other. Stokes’ theorem is also used in evaluating the curl of a vector field.