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the isoperimetric inequality says that Q ≤ 1. Equivalently, the isoperimetric ratio L2/A is at least 4π for every curve. The isoperimetric quotient of...

for all 50 states. It is possible to define a specific minimum isoperimetric quotient, proportional to the ratio between the area and the square of the...

what makes a shape compact. A common compactness measure is the isoperimetric quotient, the ratio of the area of the shape to the area of a circle (the...

infinity. Another very common shape factor is the circularity (or isoperimetric quotient), a function of the perimeter P and the area A: f circ = 4 π A P...

identical. Ball used this inequality to estimate volume ratios and isoperimetric quotients for convex sets in and. There is also a geometric version of the...

(n-1)} -sphere of radius 1. The hyperbolic space also satisfies a linear isoperimetric inequality, that is there exists a constant i {\displaystyle i} such...

goes by restating the problem as a minimization of the Rayleigh quotient. The isoperimetric inequality can be deduced from the Pólya–Szegő inequality with...

the figures have the same convex hull; the big, first hexagon. The isoperimetric problem is to determine a figure with the largest area, amongst those...

terms of the length. Mikhail Gromov once voiced the opinion that the isoperimetric inequality was known already to the Ancient Greeks. The mythological...

low degree and high expansion parameters. The edge expansion (also isoperimetric number or Cheeger constant) h(G) of a graph G on n vertices is defined...

William (1894). "Isoperimetrical problems". Nature Series: Popular Lectures and Addresses. II: 571–592. Chavel, Isaac (2001). Isoperimetric inequalities....

mentioned above, is diffusion. Among others are: the geometry of numbers, isoperimetric problems, recurrence of random walks, quadratic reciprocity, the central...

the sphere is the one having the greatest volume. It follows from isoperimetric inequality. These properties define the sphere uniquely and can be seen...

For smooth functions, this can be understood as an application of the isoperimetric inequality to the function's level sets. In one dimension, this is Wirtinger's...

physics and chemistry in statistics Exterior dimension Hurst exponent Isoperimetric dimension Metric dimension Order dimension q-dimension Fractal (q =...

assumptions. Around the same time, a similar inequality was obtained by isoperimetric methods by Mikhael Gromov, although his result is weaker than Li and...

expansion is bounded away from zero. expansion 1.  The edge expansion, isoperimetric number, or Cheeger constant of a graph G is the minimum ratio, over...

consequence of the Tits alternative). Hyperbolic groups satisfy a linear isoperimetric inequality. Hyperbolic groups are always finitely presented. In fact...

Fernando Codá Marques and André Neves. Isoperimetric inequalities. In 1939 Schmidt proved that the classical isoperimetric inequality for curves in the Euclidean...

brachistochrone problem Solution to the tautochrone problem Solution to isoperimetric problems Calculating geodesics Finding minimal surfaces and solving...