elliptisuus

Elliptisuus refers to the degree of deviation of an ellipse from being circular, or more broadly, the extent to which a shape deviates from a perfect circle or sphere. In mathematics, an ellipse is a closed curve on a plane defined as the locus of points where the sum of the distances to two fixed points (the foci) is constant. The shape of an ellipse is characterized by its semi-major axis (the longest radius) and semi-minor axis (the shortest radius), with ellipticity quantifying how elongated or flattened the ellipse is compared to a circle.

Ellipticity is often expressed as an eccentricity parameter, denoted by *e*, which ranges from 0 to 1. When *e* is 0, the ellipse is a perfect circle, and as *e* approaches 1, the ellipse becomes increasingly elongated. The eccentricity is calculated as *e* = √(1 – (b²/a²)), where *a* is the semi-major axis and *b* is the semi-minor axis. For example, an ellipse with *a* = 5 and *b* = 3 has an eccentricity of √(1 – (9/25)) ≈ 0.8, indicating a highly elongated shape.

Ellipticity is relevant in various scientific and engineering fields. In astronomy, the orbits of planets and stars are often elliptical, with ellipticity describing deviations from circular motion. In optics, elliptical polarization occurs when light waves oscillate in an elliptical pattern, characterized by their ellipticity. Additionally, in geodesy and geophysics, the Earth’s shape is approximated as an oblate spheroid, where ellipticity accounts for its slight flattening at the poles.

The concept can also extend to higher dimensions, such as ellipsoids in three-dimensional space, where ellipticity describes deviations from a spherical shape. In these cases, multiple axes (semi-major, semi-minor, and semi-intermediate) define the shape, and ellipticity may be described using multiple parameters or a generalized eccentricity measure.