Multiplication sign

The earliest known use of the {{char|×}} symbol to indicate multiplication appears in an anonymous appendix to the 1618 edition of John Napier's {{lang|la|Mirifici Logarithmorum Canonis Descriptio}}. This appendix has been attributed to William Oughtred, who used the same symbol in his 1631 algebra text, {{lang|la|Clavis Mathematicae}}, stating:

Multiplication of species [i.e. unknowns] connects both proposed magnitudes with the symbol 'in' or {{char|×}}: or ordinarily without the symbol if the magnitudes be denoted with one letter.{{cite book|url= https://books.google.com/books?id=Ld5EAAAAcAAJ | title = Clavis Mathematicae | author = William Oughtred | year= 1667 | page=10| quote = {{lang|la|Multiplicatio speciosa connectit utramque magintudinem propositam cum notâ in vel ×: vel plerumque absque notâ, si magnitudines denotentur unica litera}} }}

Other works have been identified in which crossed diagonals appear in diagrams involving multiplied numbers, such as Robert Recorde's The Ground of Arts{{cite book|last=Recorde|first=Robert|title=The Ground of Arts|year=1618|publisher=John Beale|place=London}}{{refn|The diagonals do not appear in the original 1543 edition, leaving their priority to Oughtred uncertain.}} and Oswald Schreckenfuchs's 1551 edition of Almagest, but these are not symbolizations.{{cite book|last=Cajori|first=Florian|author-link=Florian Cajori |date= 1928 | title=A History of Mathematical Notations, Volume I: Notations in Elementary Mathematics|title-link=A History of Mathematical Notations |publisher= Open Court | pages=[https://archive.org/details/historyofmathema031756mbp/page/n269 251–252] }}

In mathematics, the symbol × has a number of uses, including

• Multiplication of two numbers, where it is read as "times" or "multiplied by"
• Cross product of two vectors, where it is usually read as "cross"
• Cartesian product of two sets, where it is usually read as "cross"{{Cite web|last=Nykamp|first=Duane|title=Cartesian product definition|url=https://mathinsight.org/definition/cartesian_product|access-date=August 26, 2020|website=Math Insight}}
• 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"
• the optical magnification is sometimes referred to as "power" (for example "10× power")

In biology, the multiplication sign is used in a botanical hybrid name, 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, especially 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{{snd}} for example 1225 and 1232{{snd}} the expression "1225×1232" means "no earlier than 1225 and no later than 1232".{{citation |title=New Hart's rules: the handbook of style for writers and editors |year=2005 |publisher=Oxford University Press |isbn=978-0-19-861041-0 |page=[https://archive.org/details/newhartsrules00rmri/page/183 183] |url-access=registration |url=https://archive.org/details/newhartsrules00rmri/page/183 }}

A monadic {{char|×}} symbol is used by the APL programming language to denote the sign function.

{{Main|Multiplication#Notation|l1=Multiplication: Notation}}

The lower-case Latin letter {{char|x}} 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: "{{mvar|a}} multiplied by {{mvar|b}}" can be written as {{math|ab}} or {{math|a b}}.

Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the common variable {{mvar|x}}. In some countries, such as Germany, the primary symbol for multiplication is the "dot operator" {{char|⋅}} (as in {{math|a⋅b}}). This symbol is also used in compound units of measurement, e.g., N⋅m (see {{slink|International System of Units#Lexicographic conventions}}). In algebra, it is a notation to resolve ambiguity (for instance, "{{math|b}} times {{math|2}}" may be written as {{math|b⋅2}}, to avoid being confused with a value called {{math|b₂}}). This notation is used wherever multiplication should be written explicitly, such as in "{{math|1= ab = a⋅2}} for {{math|1=b = 2}}"; this usage is also seen in English-language texts. In some languages, the use of full stop as a multiplication symbol, such as {{math|a.b}}, is common when the symbol for decimal point is comma.

Historically, computer language syntax was restricted to the ASCII character set, and the asterisk {{char|*}} 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 {{key press|+}}, {{key press|-}}, {{key press|*}} and {{key press|/}}, respectively.

• {{unichar|00d7|MULTIPLICATION SIGN|html=}}

Other variants and related characters:

• {{unichar|002A|Asterisk|html=}}
• {{unichar|2217|Asterisk operator|html=}}
• {{unichar|2062|INVISIBLE TIMES|html=}} (a zero-width space indicating multiplication; The invisible times codepoint is used in mathematical type-setting to indicate the multiplication of two terms without a visible multiplication operator, e.g. when type-setting 2x (the multiplication of the number 2 and the variable x), the invisible times codepoint can be inserted in-between: 2 x )
• {{unichar|00B7|Middle dot|html=}} (the interpunct, may be easier to type than the dot operator)
• {{unichar|2297|CIRCLED TIMES|html=}}
• {{unichar|22C5|dot operator|html=}}
• {{unichar|2715|MULTIPLICATION X|html=}}
• {{unichar|2716|HEAVY MULTIPLICATION X|html=}}
• {{unichar|2a09|N-ARY TIMES OPERATOR|html=}}
• {{unichar|2a2f|VECTOR OR CROSS PRODUCT|html=}} (intended to explicitly denote the cross product of two vectors)
• {{unichar|2a30|MULTIPLICATION SIGN WITH DOT ABOVE|html=}}
• {{unichar|2a31|MULTIPLICATION SIGN WITH UNDERBAR|html=}}
• {{unichar|2a34|MULTIPLICATION SIGN IN LEFT HALF CIRCLE|html=}}
• {{unichar|2a35|MULTIPLICATION SIGN IN RIGHT HALF CIRCLE|html=}}
• {{unichar|2a36|CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENT|html=}}
• {{unichar|2a37|MULTIPLICATION SIGN IN DOUBLE CIRCLE|html=}}
• {{unichar|2a3b|MULTIPLICATION SIGN IN TRIANGLE|html=}}
• {{unichar|2ac1|SUBSET WITH MULTIPLICATION SIGN BELOW|html=}}
• {{unichar|2ac2|SUPERSET WITH MULTIPLICATION SIGN BELOW|html=}}

• Division sign
• List of mathematical symbols
• Plus and minus signs
• Reference mark
• X mark

{{reflist}}

• {{cite web |url=http://www.eki.ee/letter/chardata.cgi?ucode=00D7 |title=Letter Database |website=Eki.ee |access-date=2017-01-13}}
• {{cite web |url=https://www.fileformat.info/info/unicode/char/00d7/index.htm |title=Unicode Character 'MULTIPLICATION SIGN' (U+00D7) |website=Fileformat.info |access-date=2017-01-13}}
• {{cite web |url=https://www.fileformat.info/info/unicode/char/2a2f/index.htm |title=Unicode Character 'VECTOR OR CROSS PRODUCT' (U+2A2F) |website=Fileformat.info |access-date=2017-01-13}}

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Category:Mathematical symbols

Category:Multiplication