The isoperimetric problem has been extended in multiple ways, for example, to curves on surfaces and to regions in higher-dimensional spaces. Perhaps the most familiar physical manifestation of the 3 …

Dec 3, 2025 · Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle.

The isoperimetric problem (embedded in controversy) lead to the early calculus of variations. Key players were Fermat, Newton, Johann Bernoulli, and Jakob Bernoulli.

Isoperimetric problem of the calculus of variations asks for minimum of one integral functional subject to condition that another integral functional is xed. A classical example is the problem of the domain of …

Apr 21, 2021 · Motivation The isoperimetric problem, which dates back to the ancient Greeks, is to determine among all planar gures with xed perimeter the one with the largest area. The goal of the …

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 …

Jan 31, 2022 · The name "isoperimetric problem" goes back to the following classical question: Among all the curves with given perimeter in the plane, find the one that bounds the largest area.

Isoperimetric problems examine optimal relations between the size of the cut and the sizes of the separated parts. Many di erent names are used for various versions of isoperimetric problems (such …

The isoperimetric problem Tatiana Toro University of Washington Mathematics Sin Fronteras Theorem: Given a planar figure of area A and perimeter P 4⇡A P2

The first modern progress made towards the isoperimetric problem was by Swiss mathematician Jakob Steiner (1838). Though modern proofs (using calculus) are generally faster, Steiner’s proof does not …