isoperimetric(al) problem

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• Isoperimetric inequality — The isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. Isoperimetric literally means… …   Wikipedia

• Isoperimetric dimension — In mathematics, the isoperimetric dimension of a manifold is a notion of dimension that tries to capture how the large scale behavior of the manifold resembles that of a Euclidean space (unlike the topological dimension or the Hausdorff dimension …   Wikipedia

• Isoperimetric problem — In mathematics, isoperimetric problem may refer to:* The isoperimetric inequality between the length of a closed curve and the area of the region it encloses, as well as its generalizations. * Any of a class of extremal problems arising in… …   Wikipedia

• isoperimetric problem — ▪ mathematics       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.) The calculus of variations… …   Universalium

• isoperimetric — adjective Having the same perimeter; applied to the problem of finding a plane figure of the largest possible area whose boundary has a specified length …   Wiktionary

• Isoperimetrisches Problem — Das isoperimetrische Problem der geometrischen Variationsrechnung fragt in seiner ursprünglichen, auf das klassische Griechenland zurückgehenden Form (siehe Problem der Dido), welche Form eine geschlossene Kurve mit gegebener Länge haben muss,… …   Deutsch Wikipedia

• Chaplygin problem — In mathematics, particularly in the fields of nonlinear dynamics and the calculus of variations, the Chaplygin problem is an isoperimetric problem with a differential constraint. Specifically, the problem is to determine what flight path an… …   Wikipedia

• Dehn function — In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the …   Wikipedia

• Van Kampen diagram — In the mathematical area of geometric group theory, a van Kampen diagram is a planar diagram used to represent the fact that a particular word among the generators of a group given by a group presentation represents the identity element in that… …   Wikipedia

• calculus of variations — the branch of mathematics that deals with the problem of finding a curve or surface that maximizes or minimizes a given expression, usually with several restrictions placed on the desired curve. [1830 40] * * * ▪ mathematics       branch of… …   Universalium

• Geometric group theory — is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the… …   Wikipedia