Editing Diameter (section)

== Generalizations ==
The definitions given above are only valid for circles and spheres. However, they are special cases of a more general definition that is valid for any kind of <math>n</math>-dimensional object,  or a [[set (mathematics)|set]] of scattered points. The ''[[diameter of a set]]'' is the [[supremum|least upper bound]] of the set of all distances between pairs of points in the subset.

{{Anchor|Ellipse}}A different and incompatible definition is sometimes used for the diameter of a [[conic section]]. In this context, a diameter is any [[chord (geometry)|chord]] which passes through the [[center (geometry)#Projective conics|conic's centre]]. A diameter of an [[ellipse]] is any line passing through the centre of the ellipse.<ref>{{cite web|url=http://www.cut-the-knot.org/Curriculum/Geometry/ConjugateDiameters.shtml|title=Conjugate Diameters in Ellipse|first=Alexander|last=Bogomolny|website=www.cut-the-knot.org}}</ref> Half of any such diameter may be called a '''''semidiameter''''', although this term is most often a synonym for the [[radius]] of a circle or sphere.<ref>{{cite book|title=A Mathematical Dictionary|first1=Joseph|last1=Raphson|first2=Jacques|last2=Ozanam|publisher=J. Nicholson, and T. Leigh and D. Midwinter|year=1702|page=26|url=https://books.google.com/books?id=RMnn_islYKkC&pg=PA26}}</ref> The longest and shortest diameters are called the ''[[major axis]]'' and ''minor axis'', respectively. ''[[Conjugate diameters]]'' are a pair of diameters where one is parallel to a tangent to the ellipse at the endpoint of the other diameter.

Several kinds of object can be measured by ''[[equivalent diameter]]'', the diameter of a circular or spherical approximation to the object. This includes [[hydraulic diameter]], the equivalent diameter of a channel or pipe through which liquid flows, and the [[Sauter mean diameter]] of a collection of particles.

The diameter of a circle is exactly twice its radius. However, this is true only for a circle, and only in the [[Euclidean distance|Euclidean metric]]. [[Jung's theorem]] provides more general inequalities relating the diameter to the radius.