Eccentricity (mathematics) - Definition and Overview

(This page refers to eccitricity in mathematics. For other uses, see the disambiguation page eccentricity.)

In mathematics, eccentricity is a parameter associated with every conic section, see Conic section#Eccentricity. It can be thought of as a measure of how much the conic section deviates from being circular. In particular,

• The eccentricity of a circle is zero.
• The eccentricity of an ellipse is greater than zero and less than 1.
• The eccentricity of a parabola is 1.
• The eccentricity of a hyperbola is greater than 1.
• The eccentricity of a straight line is infinity.

Ellipse

For any ellipse, where the length of the semi-major axis is a, and where the same of the semi-minor axis is b, the eccentricity is given by

<math>e = \sqrt{1-\frac{b^2}{a^2}}.<math>

The eccentricity is the ratio of the distance between the foci (<math>F_1<math> and <math>F_2<math>) to the major axis; i.e. <math>\left ( \frac{\overline{F_1F_2}}{\overline{AB}} \right ).<math>

The term linear eccentricity is used for <math>{ea}.<math>

Hyperbola

For any hyperbola, where the length of the semi-major axis is a, and where the same of the semi-minor axis is b, eccentricity is given by

<math>e = \sqrt{1+\frac{b^2}{a^2}}.<math>

External links

• MathWorld: Eccentricity (http://mathworld.wolfram.com/Eccentricity.html)