Diameter

In geometry, the diameter of a circle is the length of a straight line segment that passes from a point on the circle to the opposite point (and therefore passes through the centre of the circle). This length is twice the radius. The line segment itself is also called a diameter.

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 } .

The symbol or variable for diameter is similar in size and design to ø, 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 ø is acceptable, obtained in Windows by holding the [Alt] key down while entering 0 2 4 8 on the numeric keypad. A magnified version of a diameter symbol is shown at right.

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