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Diameter

In geometry, a diameter (Greek words diairo=divide and metro=count/measure) of a circle is any straight line segment that passes through the center and whose endpoints are on the circular boundary, or, in more modern usage, the length of such a line segment. When using the word in the more modern sense, one speaks of the diameter rather than a diameter, because all diameters of a circle have the same length. This length is twice the radius.

The diameter of a connected graph is the distance between the two vertices which are furthest from each other. The distance between two vertices a and b is the length of the shortest path connecting them (for the length of a path, see Graph theory).

The two 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

sup { d(x, y) | x, y in A } .

Diameter symbol


The symbol or variable for diameter is similar in size and design to , the lowercase letter o with stroke. Unicode provides character number 8960 (hexadecimal 2300) for the symbol, which can be encoded in HTML webpages as ⌀ or ⌀. Proper display of this character, however, is unlikely in most situations, as most fonts do not have it included. (Your browser displays ⌀ and ⌀ in the current font.) In most situations the letter is acceptable, obtained in Windows by holding the [Alt] key down while entering 0 2 4 8 on the numeric keypad.

It is important not to confuse a diameter symbol () with the empty set symbol, similar to the uppercase . Diameter is also sometimes called phi (pronounced the same as "fee"), although this seems to come from the fact that and look like Φ and φ, the letter phi in the Greek alphabet.

See also: angular diameter, hydraulic diameter


Last updated: 02-08-2005 16:17:35
Last updated: 02-11-2005 17:47:38