 a vinculum is a horizontal line used in mathematical notation. it may be placed as an overline over a mathematical expression to indicate that the expression is to be considered grouped together, or alternatively it may function as a binary connective between arguments appearing above and below it, in particular as a fraction bar. vinculum is latin for "bond", "fetter", "chain", or "tie", which is roughly suggestive of some of the uses of the symbol. the vinculum was developed in the 12th century by the moroccan mathematician abu bakr al-hassar.. ==uses==  the vinculum can be used to express division. the numerator appears above the vinculum and the denominator beneath it. vulgar fractions are a common special case of this usage. :\frac{1}{3} in a repeating decimal, the vinculum is used to indicate the group of repeating digits: :\frac{1}{3} = 0.333\dots = 0.\overline{3} ; &nbsp; &nbsp; \frac{1}{11} = 0.0909\dots = 0.\overline{09}. 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 ab+2 is the radicand, and thus has a vinculum over it: :\sqrt[n]{ab+2} 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: :\pi \approx 10.011\overline{1}111\overline{1}000\overline{1}011\overline{1}1101\overline/11111100\overline{1}0000\overline{1}1\overline{1}\overline{1}\overline{1}\overline{1}0\overline{1} 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: :\overline{ab}. it is also used to refer to the conjugate of a complex number: :\bar{z} = \overline{x+iy} = {x-iy} it can even be used as a notation to indicate a group (bracket similar to parenthesis): :(a-\overline{b+c}) 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  are the symbols for proton and antiproton, respectively. the vinculum should not be confused with a similar-looking vector notation, e.g. \overright
Elementary_mathematics Mathematical_symbols