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| ==Mathematics== | ==Mathematics== | ||
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| 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 of ellipse |
:<math>\mbox{eccentricity of ellipse: } e = \sqrt{1-\frac{b^2}{a^2}}</math> | ||
| For any hyperbola, where the length of the ] is ''a'', and where the same of the ] is ''b'': | For any hyperbola, where the length of the ] is ''a'', and where the same of the ] is ''b'': | ||
| :<math>\mbox{eccentricity of hyperbola |
:<math>\mbox{eccentricity of hyperbola: } e = \sqrt{1+\frac{b^2}{a^2}}</math> | ||
| ===External Links=== | ===External Links=== | ||
Revision as of 19:17, 3 March 2004
Mathematics
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:
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.
Extravagance is a kind of eccentricity, related to abundance and wastefulness.