The multiplication sign, also known as the times sign or the dimension sign, is the symbol , used in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

to denote the multiplication operation and its resulting product. While similar to a lowercase X (), the form is properly a four-fold

rotationally symmetric Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which i ...

saltire.

History

The earliest known use of the symbol to represent multiplication appears in an anonymous appendix to the 1618 edition of John Napier's . This appendix has been attributed to William Oughtred, who used the same symbol in his 1631 algebra text, , stating:

"Multiplication of species .e. unknownsconnects both proposed magnitudes with the symbol 'in' or : or ordinarily without the symbol if the magnitudes be denoted with one letter."

Two earlier uses of a notation have been identified, but do not stand critical examination.

Uses

, the

symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...

× has a number of uses, including *

Multiplication Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...

of two numbers, where it is read as "times" or "multiplied by" *

Cross product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is ...

of two vectors, where it is usually read as "cross" *

Cartesian product In mathematics, specifically set theory, the Cartesian product of two sets ''A'' and ''B'', denoted ''A''×''B'', is the set of all ordered pairs where ''a'' is in ''A'' and ''b'' is in ''B''. In terms of set-builder notation, that is : A\ti ...

of two sets, where it is usually read as "cross" * Geometric dimension of an object, such as noting that a room is 10 feet × 12 feet in area, where it is usually read as "by" (e.g., "10 feet by 12 feet") * Screen resolution in pixels, such as 1920 pixels across × 1080 pixels down. Read as "by". * Dimensions of a matrix, where it is usually read as "by" * A statistical interaction between two explanatory variables, where it is usually read as "by" In biology, the multiplication sign is used in a botanical

hybrid name In botanical nomenclature, a hybrid may be given a hybrid name, which is a special kind of botanical name, but there is no requirement that a hybrid name should be created for plants that are believed to be of hybrid origin. The '' International C ...

, for instance ''Ceanothus papillosus'' × ''impressus'' (a hybrid between '' C. papillosus'' and '' C. impressus'') or '' Crocosmia × crocosmiiflora'' (a hybrid between two other species of ''Crocosmia''). However, the communication of these hybrid names with a Latin letter "x" is common, when the actual "×" symbol is not readily available. The multiplication sign is also used by historians for an event between two dates. When employed between two dates for example 1225 and 1232 the expression "1225×1232" means "no earlier than 1225 and no later than 1232". A monadic symbol is used by the

APL programming language APL (named after the book ''A Programming Language'') is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols to represent mos ...

to denote the

sign function In mathematics, the sign function or signum function (from '' signum'', Latin for "sign") is an odd mathematical function that extracts the sign of a real number. In mathematical expressions the sign function is often represented as . To avoi ...

Similar notations

The lower-case Latin letter is sometimes used in place of the multiplication sign. This is considered incorrect in mathematical writing. In algebraic notation, widely used in mathematics, a multiplication symbol is usually omitted wherever it would not cause confusion: " multiplied by " can be written as or . Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the common variable . In some countries, such as Germany, the primary symbol for multiplication is the " dot operator" (as in '). This symbol is also used in algebraic notation to resolve ambiguity (for instance, "b times 2" may be written as , to avoid being confused with a value called ). This notation is used wherever multiplication should be written explicitly, such as in " for "; this usage is also seen in English-language texts. In some languages, the use of

full stop The full stop (Commonwealth English), period (North American English), or full point , is a punctuation mark. It is used for several purposes, most often to mark the end of a declarative sentence (as distinguished from a question or exclamation ...

as a multiplication symbol, such as , is common when the symbol for decimal point is

comma The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline ...

. Historically, computer language

syntax In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure ( constituency) ...

was restricted to the ASCII character set, and the

asterisk The asterisk ( ), from Late Latin , from Ancient Greek , ''asteriskos'', "little star", is a typographical symbol. It is so called because it resembles a conventional image of a heraldic star. Computer scientists and mathematicians often voc ...

became the de facto symbol for the multiplication operator. This selection is reflected in the numeric keypad on English-language keyboards, where the arithmetic operations of addition, subtraction, multiplication and division are represented by the keys , , and , respectively.

Typing the character

Unicode and HTML entities

* Other variants and related characters: * * (a zero-width space indicating multiplication) * (the

interpunct An interpunct , also known as an interpoint, middle dot, middot and centered dot or centred dot, is a punctuation mark consisting of a vertically centered dot used for interword separation in ancient Latin script. (Word-separating spaces did no ...

, may be easier to type than the dot operator) * * * * * * (intended to ''explicitly'' denote the

cross product In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is ...

of two vectors) * * * * * * * * *

References

External links

* * * {{navbox punctuation Mathematical symbols Multiplication