# Diameter

A diameter of a second-order curve is a straight line passing through the midpoints of parallel chords. The diameter is said to be conjugate with respect to the chords (and with respect to the directions of the chords) bisected by it. Diameters of a central curve of the second order intersect each other at the midpoint of the curve; diameters of non-central curves of the second order are parallel (or coincide). The diameters of an ellipse and of a hyperbola are straight lines passing through their centre. The diameters of a parabola are the axis of the parabola and the straight lines parallel to it.

The diameter of a set in a metric space is the least upper bound of the distances between pairs of points of the set.

**How to Cite This Entry:**

Diameter. A.B. Ivanov (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Diameter&oldid=13266