Eccentricity (mathematics)

In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape.

For the eccentricity of a vertex in a graph, see Eccentricity (graph theory).

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Alternative names[edit]

In the case of ellipses and hyperbolas the half-focal separation is sometimes called the linear eccentricity.

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One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular:

Two conic sections with the same eccentricity are similar.

A number of classifications in mathematics use derived terminology from the classification of conic sections by eccentricity:

Hyperbolas[edit]

The eccentricity of a hyperbola can be any real number greater than 1, with no upper bound. The eccentricity of a rectangular hyperbola is ${\sqrt {2}}$ .

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of SL₂(R) as elliptic, parabolic, and hyperbolic – and similarly for classification of elements of PSL₂(R), the real Möbius transformations.

Classification of elements

Classification of discrete distributions by ; see cumulants of some discrete probability distributions for details.

variance-to-mean ratio

Classification of is by analogy with the conic sections classification; see elliptic, parabolic and hyperbolic partial differential equations.^[3]

partial differential equations

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Kepler orbits

Eccentricity vector

Orbital eccentricity

Roundness (object)

Conic constant

MathWorld: Eccentricity

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