Diameter

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In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle. The word "diameter" derives from Greek διάμετρος (diametros), "diagonal of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "a measure"[1]).

In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length, this being twice the radius.

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 defined to be the smallest such distance. 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. See also Tangent lines to circles.

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Generalizations

The three definitions given above are special cases of a more general definition. The diameter of a subset of a metric space is the least upper bound of the distances between pairs of points in the subset. So, if A is the subset, the diameter is

Some authors prefer to treat the empty set ($A=\emptyset$) as a special case.[2]

In differential geometry, the diameter is an important global Riemannian invariant. In plane and coordinate geometry, a diameter of a conic section is any chord which passes through the conic's centre; such diameters are not necessarily of uniform length, except in the case of the circle, which has eccentricity e = 0.

In medical parlance the diameter of a lesion is the longest line segment whose endpoints are within the lesion.

Diameter symbol

The symbol or variable for diameter, , is similar in size and design to ø, the Latin small letter o with stroke. Unicode provides character number 8960 (hexadecimal 2300) for the symbol, which can be encoded in HTML webpages as &#8960; or &#x2300;. The character can be obtained in Microsoft Windows by holding the [Alt] key down while entering 8 9 6 0 on the numeric keypad. On an Apple Inc. Macintosh, the diameter symbol can be entered via the character palette (this is opened by pressing T in most applications), where it can be found in the Technical Symbols category.