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In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: The eccentricity of a circle is 0. The eccentricity of an ellipse which is not a circle is between 0 and 1.
The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in symbols, = (,). It can be thought of as how far a node is from the node most distant from it in the graph. The radius r of a graph is the minimum eccentricity of any vertex or, in symbols,
An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It is denoted here by α (alpha). It may be defined in terms of the eccentricity , e , or the aspect ratio, b/a (the ratio of the semi-minor axis and the semi-major axis ):
a plane angle in geometry; the angle to the x axis in the xy-plane in spherical or cylindrical coordinates (mathematics) the angle to the z axis in spherical coordinates (physics) the potential temperature in thermodynamics; theta functions; the angle of a scattered photon during a Compton scattering interaction
Roundness is dominated by the shape's gross features rather than the definition of its edges and corners, or the surface roughness of a manufactured object. A smooth ellipse can have low roundness, if its eccentricity is large. Regular polygons increase their roundness with increasing numbers of sides, even though they are still sharp-edged.
The eccentricity e is defined as: = . From Pythagoras's theorem applied to the triangle with r (a distance FP) as hypotenuse: = + () = () + ( + ) = + = () Thus, the radius (distance from the focus to point P) is related to the eccentric anomaly by the formula
Horizontal eccentricity, in vision, degrees of visual angle from the center of the eye; Eccentric contraction, the lengthening of muscle fibers; Eccentric position of a surveying tripod, to be able to measure hidden points; Eccentric training, the motion of an active muscle while it is lengthening under load; Eccentricity, a deviation from ...