Vinculum (symbol) - Uses

Uses

The vinculum can be used to express division. The dividend appears above the vinculum and the divisor beneath it. Vulgar fractions are a common special case of this usage.

In a repeating decimal, the vinculum is used to indicate the group of repeating digits:

It is used as part of the notation of a radical to indicate the radicand whose root is being indicated. In the next case, the quantity is the radicand, and thus has a vinculum over it:

It is used to show the repeating terms in a periodic continued fraction. Quadratic irrational numbers are the only numbers that have these.

It can be used in signed-digit representation to represent negative digits, such as the following example in balanced ternary:

The vinculum is sometimes used in Boolean algebra, where it serves to indicate a group of expressions whose logical result is to be negated, as in:

It is also used to refer to the conjugate of a complex number:

It can even be used as a notation to indicate a group (bracket smaller to parenthesis):

meaning to add b and c first and then subtract the result from a.

In statistics the vinculum can be used to indicate the mean of series of values.

In particle physics, the vinculum is used to indicate antiparticles. For example, p and p are the symbols for proton and antiproton, respectively.

The vinculum should not be confused with a similar-looking vector notation, e.g. "vector from A to B", or "vector named a".