In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere.
In more modern usage, the length
d
r.
d=2r orequivalently r=
d | |
2 |
.
For a convex shape in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary, and the is often defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers.[1] For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.
For an ellipse, the standard terminology is different. A diameter of an ellipse is any chord passing through the centre of the ellipse.[2] For example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one diameter is parallel to the conjugate diameter. The longest diameter is called the major axis.
The word "diameter" is derived from Greek, Ancient (to 1453);: διάμετρος, "diameter of a circle", from Greek, Ancient (to 1453);: διά, "across, through" and Greek, Ancient (to 1453);: μέτρον, "measure".[3] It is often abbreviated
DIA,dia,d,
\varnothing.
The definitions given above are only valid for circles, spheres and convex shapes. However, they are special cases of a more general definition that is valid for any kind of
n
S
\rho
If the metric
\rho
\R
S=\varnothing
-infty
0,
\rho
For any solid object or set of scattered points in
n
In differential geometry, the diameter is an important global Riemannian invariant.
e=0.
The symbol or variable 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.[5] Photographic filter thread sizes are often denoted in this way.[6]
The symbol has a Unicode code point at, in the Miscellaneous Technical set, and should not be confused with several other Unicode characters that resemble it but have unrelated meanings.[7] It has the compose sequence .[8]
The diameter of a circle is exactly twice its radius. However, this is true only for a circle, and only in the Euclidean metric. Jung's theorem provides more general inequalities relating the diameter to the radius.