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| * The eccentricity of a ] is ]. | * The eccentricity of a ] is ]. | ||
| For any ellipse, where the length of the ] is ''a'', and where the same of the ] is ''b'': | For any ellipse, where the length of the ] is ''a'', and where the same of the ] is ''b'': | ||
| :<math>\mbox{eccentricity} = e = \sqrt{1-\frac{b^2}{a^2}}</math> | :<math>\mbox{eccentricity} = e = \sqrt{1-\frac{b^2}{a^2}}</math> | ||
Revision as of 18:56, 20 February 2004
In mathematics, eccentricity is a parameter associated with every conic section. 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.
For any ellipse, where the length of the semi-major axis is a, and where the same of the semi-minor axis is b:
In astronomy, the eccentricity of an orbit can be calculated using this formula. For example, the eccentricity of the Earth's orbit is 0.0167.
In popular usage, eccentricity refers to unusual or odd behavior on the part of a person, as opposed to being normal. Eccentric behavior is often considered whimsical or quirky, although it can also be strange and disturbing. American millionaire Howard Hughes, for example was considered to be very eccentric, and stored his urine in glass jars and never cut his hair or nails. Other people may have eccentric taste in clothes, or have eccentric hobbies or collections.
Many of history's most brilliant minds have displayed many unusual behaviors and habits, and eccentricity is sometimes thought to be a sign of genius. However, many eccentrics are cranks, rather than geniuses.
Extravagance is a kind of eccentricity, related to abundance and wastefulness.