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| ==Mathematics== | ==Mathematics== | ||
| In ], '''eccentricity''' is a parameter associated with every ]. It can be thought of as a measure of how much the conic section deviates from being circular. In particular: | In ], '''eccentricity''' is a parameter associated with every ], see ]. It can be thought of as a measure of how much the conic section deviates from being circular. In particular: | ||
| * The eccentricity of a ] is zero. | * The eccentricity of a ] is zero. | ||
| * The eccentricity of an ] is greater than zero and less than 1 | * The eccentricity of an ] is greater than zero and less than 1 | ||
Revision as of 09:35, 8 May 2004
Mathematics
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.
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 dimensionless numerical eccentricity (called simply eccentricity hereafter) is shown using the greek letter epsilon to avoid confusion with the symbol , which will represent the linear eccentricity:
to avoid confusion with the symbol 
, which will represent the linear eccentricity:
Which is equivalent to stating that the eccentricity is the ratio of the distance between the foci (F1 and F2) to the major axis, a:
For any hyperbola, where the length of the semi-major axis is a, and where the same of the semi-minor axis is b:
External Links
Mathworld: Eccentricity
Astronomy
In astronomy, the eccentricity of an orbit can be calculated using the formulas above if the shape of the orbit is known.
For example, the eccentricity of the Earth's orbit is 0.0167.
Orbital eccentricity can also be calculated using other methods based on orbital energy and angular momentum.
External Links
World of Physics: Eccentricity
Popular Usage
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.
John Stuart Mill says in his philosophical work "On Liberty", that the existence of eccentricity within a society is not only possible, it is essential. This bohemian personage, similar to that described by Rousseau, is in fact a great benefit to their society. A society without this is a stagnant society. Is it preferable to remain stagnant, ignorant but happy? According to the categorical imperative of Kant, it <--? WHAT? -->is a crime against oneself. Extravagance is a kind of eccentricity, related to abundance and wastefulness.