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isoperimetric and inequality
In every polygon with perimeter p and area A, the isoperimetric inequality holds.
In mathematics, 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.
Specifically, the isoperimetric inequality states, for the length L of a closed curve and the area A of the planar region that it encloses, that
Perhaps the most familiar physical manifestation of the 3-dimensional isoperimetric inequality is the shape of a drop of water.
The solution to the isoperimetric problem is usually expressed in the form of an inequality that relates the length L of a closed curve and the area A of the planar region that it encloses.
Dozens of proofs of the isoperimetric inequality have been found.
and the isoperimetric inequality says that Q ≤ 1.
Denote by L the length of C and by A the area enclosed by C. The spherical isoperimetric inequality states that
In full generality, the isoperimetric inequality states that for any set S ⊂ R < sup > n </ sup > whose closure has finite Lebesgue measure
The isoperimetric inequality in n-dimensions can be quickly proven by the Brunn-Minkowski inequality (; ).
The n-dimensional isoperimetric inequality is equivalent ( for sufficiently smooth domains ) to the Sobolev inequality on R < sup > n </ sup > with optimal constant:
The edge isoperimetric inequality of the hypercube is.
* Gaussian isoperimetric inequality
* Treiberg: Several proofs of the isoperimetric inequality
# redirect isoperimetric inequality
By the isoperimetric inequality and Barbier's theorem, the circle has the maximum area of any curve of given constant width.
Among others are: the geometry of numbers, isoperimetric problems, recurrence of random walks, quadratic reciprocity, the central limit theorem, Heisenberg's inequality.
In the Euclidean space, the isoperimetric inequality says that of all bodies with the same volume, the ball has the smallest surface area.
We say about a manifold M that it satisfies a d-dimensional isoperimetric inequality if for any open set D in M with a smooth boundary one has
The isoperimetric dimension of M is the supremum of all values of d such that M satisfies a d-dimensional isoperimetric inequality.

inequality and states
The inequality states that
" Also known as the kinship theory of genomic imprinting, this hypothesis states that the inequality between parental genomes due to imprinting is a result of the differing interests of each parent in terms of the evolutionary fitness of their genes.
Samuelson's inequality is a result that states, given that the sample mean and variance have been calculated from a particular sample, bounds on the values that individual values in the sample can take.
The Cauchy – Schwarz inequality states that for all vectors x and y of an inner product space it is true that
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side ( and, if the setting is a Euclidean space, then the inequality is strict if the triangle is non-degenerate ).< ref name = Khamsi >
For instance, Daisy Myers has been hailed as " The Rosa Parks of the North ", who helped expose the northern states ' problems with racial inequality of that time.
The Chebyshev inequality states that if is a random variable with standard deviation σ, then the probability that the outcome of is no less than away from its mean is no more than:
Markov's inequality states that for any real-valued random variable Y and any positive number a, we have Pr (| Y | > a ) ≤ E (| Y |)/ a.
In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics cannot be reproduced by local hidden variable theories.
It would appear from both these later derivations that the only assumptions really needed for the inequality itself ( as opposed to the method of estimation of the test statistic ) are that the distribution of the possible states of the source remains constant and the detectors on the two sides act independently.
An equivalent formulation states that for any ε > 0, there exists a constant K such that, for all triples of coprime positive integers ( a, b, c ) satisfying a + b = c, the inequality
In the language of measure theory, Markov's inequality states that if ( X, Σ, μ ) is a measure space, ƒ is a measurable extended real-valued function, and, then
This provides an interesting twist on Wallerstein's neo-Marxist interpretation of the international order which faults differences in power relations between ' core ' and ' periphery ' states as the chief cause for economic and political inequality ( However, the Singer-Prebisch thesis also works with different bargaining positions of labour in developed and developing countries ).
# The Bishop – Gromov inequality states that if a complete m-dimensional Riemannian manifold has non-negative Ricci curvature, then the volume of a ball is smaller or equal to the volume of a ball of the same radius in Euclidean m-space.
In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean after convex transformation ; it is a simple corollary that the opposite is true of concave transformations.
Each inequality states that your opponent's net gain is more than zero.
On the issue of markets in a socialist society, Webb states, " Admittedly, market mechanisms in a socialist society can generate inequality, disproportions and imbalances, destructive competition, downward pressure on wages, and monopoly cornering of commodity markets – even the danger of capitalist restoration.
Specifically, the Koksma-Hlawka inequality states that the error
The geodesic minimizes the entropy, due to the Cauchy – Schwarz inequality, which states that the action is bounded below by the length of the curve, squared.
Then Bernstein's inequality states that for M non-zero,

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