Ingeometry, adiameter of acircle is any straightline segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longestchord of the circle. Both definitions are also valid for the diameter of asphere.
In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks ofthe diameter rather thana diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice theradius
The word "diameter" is derived fromAncient Greek:διάμετρος (diametros), "diameter of a circle", fromδιά (dia), "across, through" andμέτρον (metron), "measure".[1] It is often abbreviated or
Withstraightedge and compass, a diameter of a given circle can be constructed as theperpendicular bisector of an arbitrary chord. Drawing two diameters in this way can be used to locate the center of a circle, as their crossing point.[2] To construct a diameter parallel to a given line, choose the chord to be perpendicular to the line.
The circle having a given line segment as its diameter can be constructed by straightedge and compass, by finding themidpoint of the segment and then drawing the circle centered at the midpoint through one of the ends of the line segment.
Sign ⌀ in a technical drawingAphotographic filter marked as having a 58mm thread diameter
Thesymbol orvariable for diameter,⌀, is sometimes used in technical drawings or specifications as a prefix or suffix for a number (e.g. "⌀ 55 mm"), indicating that it represents diameter.[3] Photographicfilter thread sizes are often denoted in this way.[4]
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-dimensional object, or aset of scattered points. Thediameter of a set is theleast upper bound of the set of all distances between pairs of points in the subset.
A different and incompatible definition is sometimes used for the diameter of aconic section. In this context, a diameter is anychord which passes through theconic's centre. A diameter of anellipse is any line passing through the centre of the ellipse.[7] Half of any such diameter may be called asemidiameter, although this term is most often a synonym for theradius of a circle or sphere.[8] The longest diameter is called themajor axis.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 byequivalent diameter, the diameter of a circular or spherical approximation to the object. This includeshydraulic diameter, the equivalent diameter of a channel or pipe through which liquid flows, and theSauter 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 theEuclidean metric.Jung's theorem provides more general inequalities relating the diameter to the radius.
^"6-66 Finding the center of a circle".General Drafting. Technical manual, TM 5-581A, United States Department of the Army. U.S. Government Printing Office. 1972. p. 6-32.
^Ciaglia, Joseph (2002).Introduction to Digital Photography. Prentice Hall. p. 9.ISBN9780130321367.The filter diameter (in mm) usually follows the symbol ⌀
