Eccentricity

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.

Ellipse showing foci, axes, and linear eccentricity

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

${\mbox{eccentricity of ellipse: }}\epsilon ={\sqrt {1-{\frac {b^{2}}{a^{2}}}}}$

The dimensionless numerical eccentricity (called simply eccentricity hereafter) is shown using the greek letter epsilon ${\boldsymbol {\epsilon }}$ to avoid confusion with the symbol ${\boldsymbol {e}}$ , which will represent the linear eccentricity:

${\mbox{linear eccentricity of ellipse: }}{e}=\epsilon {a}$

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:

${\mbox{eccentricity of ellipse: }}\epsilon ={\frac {2e}{2a}}$

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

${\mbox{eccentricity of hyperbola: }}\epsilon ={\sqrt {1+{\frac {b^{2}}{a^{2}}}}}$

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 today is 0.0167. Through time, the eccentricity of the Earth's orbit slowly changes from nearly 0 to almost 0.05 as a result of gravitational attractions between the planets (see graph [1]).

Orbital eccentricity can also be calculated using other methods based on orbital energy and angular momentum.

External links

• World of Physics: Eccentricity

Mechanics

In mechanical engineering, an eccentric is a wheel that rotates on an axle that is displaced from the focus of the circle described by the wheel; in other words, a mechanical motion that can operate either as a cam or a crank, depending upon how it is driven.

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 in his old age, when he 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 is a crime against oneself.

Extravagance is a kind of eccentricity, related to abundance and wastefulness.

For extravagant text, see also hyperbole.

List of notable eccentrics