Diameter

Circle with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre or origin (O) in green.

In geometry, a diameter of a circle is any straight line segment that passes through the center 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.

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 width 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.

In differential geometry, the diameter is an important global Riemannian invariant.

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. For example, photographic filter thread sizes are often denoted in this way.

In German, the diameter symbol (German Durchmesserzeichen) is also used as an average symbol (Durchschnittszeichen).

It is similar in size and design to ø, the Latin small letter o with stroke. The diameter symbol ⌀ is distinct from the empty set symbol , from an (italic) uppercase phi Φ, and from the Nordic vowel Ø (Latin capital letter O with stroke).[5] See also slashed zero.

The symbol has a Unicode code point at U+2300 DIAMETER SIGN (HTML ⌀), in the Miscellaneous Technical set. On an Apple Macintosh, the diameter symbol can be entered via the character palette (this is opened by pressing ⌥ Opt⌘ CmdT in most applications), where it can be found in the Technical Symbols category. In Unix/Linux/ChromeOS systems, it is generated using ctrl+⇧ Shift+u 2300space It can be obtained in UNIX-like operating systems using a Compose key by pressing, in sequence, Composedi[6]

The character will sometimes not display correctly, however, since many fonts do not include it. In many situations the letter ø (the Latin small letter o with stroke) is an acceptable substitute, which in Unicode is U+00F8 ø (HTML ø · ø). and on a Macintosh by pressing ⌥ Opt O (the letter o, not the number 0). In Unix/Linux/ChromeOS systems, it is generated using ctrl+⇧ Shift+u F8space or Composeo/. AutoCAD uses U+2205 EMPTY SET available as a shortcut string %%c.

In Microsoft Word the diameter symbol can be acquired by typing 2300 and then pressing Alt+X.

In LaTeX the diameter symbol can be obtained with the command \diameter from the wasysym package.