nearsphericity

Nearsphericity refers to the property of a shape or object being close to a sphere. In practice, it is quantified by comparing the shape to a ball of the same size using geometric metrics. Common approaches include measuring how far the boundary is from a perfect sphere, for example by the Hausdorff distance between the surface and a spherical surface, or by examining the radial deviation of a surface from a central radius.

A widely used scalar measure is the sphericity, defined for a body with volume V and surface area S as φ = π^(1/3) (6V)^(2/3) / S. This index equals 1 for a perfect sphere and decreases as a shape becomes less sphere-like. Another simple descriptor is the flattening or oblateness parameter, such as f = (a − c)/a for ellipsoids with axes a ≥ b ≥ c; small f indicates near-sphericity. A related concept is the isoperimetric deficit, which compares the surface area to the minimum possible for a given volume; small deficits imply closeness to a ball, a relation formalized in quantitative stability results.

In mathematics, near-sphericity often arises in the study of domains that approximate balls. The isoperimetric inequality and its stability theorems show that shapes with small surface-area-to-volume excess are close to a sphere in a precise sense. In applied contexts, near-spherical objects include droplets held by surface tension, small planets and asteroids with modest rotation, and biological cells, where deviations from sphericity reflect physical forces or growth processes.

Overall, nearsphericity describes how little a given object deviates from a perfect sphere, with several compatible metrics to quantify the closeness.