# diameter

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## diameter

a. a straight line connecting the centre of a geometric figure, esp a circle or sphere, with two points on the perimeter or surface
b. the length of such a line

## Diameter

The diameter of a circle is the chord that passes through the center of the circle. Moreover, the diameter of a circle is the length of this chord, equal to two radii.

In analytic geometry the diameter of a conic section (or of a curve of the second order) is understood to mean the straight line that passes through the midpoints of a set of parallel chords. For central curves of the second order (circles, ellipses, hyperbolas) this is the straight line passing through the center of the curve. In the case of the parabola, all diameters are parallel to its axis.

The concept of the diameter of a circle as the length of a segment is applied to other geometric figures and to sets of a more general nature. The diameter of a figure (or a set in metric space) is precisely the upper bound of the distances between all possible pairs of points of this figure. In this sense, the diameter of an ellipse is equal to the length of the semimajor axis, and the diameter of a square is equal to the length of its diagonal.

## diameter

[dī′am·əd·ər]
(mathematics)
A line segment which passes through the center of a circle, and whose end points lie on the circle.
The length of such a line.
For a conic, any straight line that passes through the midpoints of all the chords of the conic that are parallel to a given chord.
For a set, the smallest number that is greater than or equal to the distance between every pair of points of the set.

## diameter

The diameter of a graph is the maximum value of the minimum distance between any two nodes.

## Diameter

An authentication, authorization and accounting (AAA) protocol that replaces RADIUS (Diameter is a play on the word RADIUS). Like RADIUS, Diameter uses a challenge/response method; however, unlike RADIUS, Diameter uses the reliable TCP and SCTP protocols rather than the unreliable UDP for transport. Diameter also supports error reporting and is better at scaling than RADIUS. See RADIUS, network access server and challenge/response.
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