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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.
In orbital mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit.The eccentric anomaly is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the true anomaly and the mean anomaly.
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 ):
It is also possible to describe all conic sections in terms of a single focus and a single directrix, which is a given line not containing the focus. A conic is defined as the locus of points for each of which the distance to the focus divided by the distance to the directrix is a fixed positive constant, called the eccentricity e.
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,
The usual notation for flattening is and its definition in terms of the semi-axes and of the resulting ellipse or ellipsoid is f = a − b a . {\displaystyle f={\frac {a-b}{a}}.} The compression factor is b / a {\displaystyle b/a} in each case; for the ellipse, this is also its aspect ratio .
The numbers show each node's eccentricity. In the mathematical subfield of graph theory, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers. Given a graph, the eccentricity of a vertex v is defined as the greatest distance from v to any other vertex. A center of a graph is a vertex with minimal ...
The center (or Jordan center [1]) of a graph is the set of all vertices of minimum eccentricity, [2] that is, the set of all vertices u where the greatest distance d(u,v) to other vertices v is minimal. Equivalently, it is the set of vertices with eccentricity equal to the graph's radius. [3]