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 Product may refer to: Business * Product (business), an item that serves as a solution to a specific consumer problem. * Product (project management), a deliverable or set of deliverables that contribute to a business solution Mathematics * Produ ...

. While similar to a lowercase X (), the form is properly a four-fold rotationally symmetric

saltire A saltire, also called Saint Andrew's Cross or the crux decussata, is a heraldic symbol in the form of a diagonal cross, like the shape of the letter X in Roman type. The word comes from the Middle French ''sautoir'', Medieval Latin ''saltatori ...

History

The earliest known use of the symbol to represent multiplication appears in an anonymous appendix to the 1618 edition of

John Napier John Napier of Merchiston (; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioan ...

's . This appendix has been attributed to

William Oughtred William Oughtred ( ; 5 March 1574 – 30 June 1660), also Owtred, Uhtred, etc., was an Kingdom of England, English mathematician and Anglican ministry, Anglican clergyman.'Oughtred (William)', in P. Bayle, translated and revised by J.P. Bernar ...

, 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 Multiplication sign, cross symbol , by the mid-line #Notation and terminology, dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four Elementary arithmetic, elementary Op ...

of two

numbers A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...

, 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 ...

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\t ...

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 Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchi ...

, where it is usually read as "by" * A statistical interaction between two explanatory variables, where it is usually read as "by" In

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...

, 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 Cod ...

, 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

historian A historian is a person who studies and writes about the past and is regarded as an authority on it. Historians are concerned with the continuous, methodical narrative and research of past events as relating to the human race; as well as the st ...

s 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 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 avo ...

Similar notations

The lower-case Latin letter is sometimes used in place of the multiplication sign. This is considered incorrect in mathematical writing. In

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

ic 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 Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...

, the primary symbol for multiplication is the "

dot operator 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 addi ...

" (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 exclamatio ...

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

decimal point A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choi ...

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 ( constituenc ...

was restricted to the

ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...

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 A numeric keypad, number pad, numpad, or ten key, is the palm-sized, usually-17-key section of a standard computer keyboard, usually on the far right. It provides calculator-style efficiency for entering numbers. The idea of a 10-key nu ...

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 n ...

, 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 ...

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

References

External links

* * * {{navbox punctuation Mathematical symbols Multiplication