Multiplication sign

The multiplication sign (Template:Char), also known as the times sign or the dimension sign, is a mathematical symbol used to denote the operation of multiplication, which results in a product.<ref name=":1">{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

The symbol is also used in botany, in botanical hybrid names.

The form is properly a four-fold rotationally symmetric saltire.<ref>Template:Cite journal</ref> The multiplication sign Template:Char is similar to a lowercase X (Template:Char).

History

The earliest known use of the Template:Char symbol to indicate multiplication appears in an anonymous appendix to the 1618 edition of John Napier's {{#invoke:Lang|lang}}.<ref name=Cajori /> This appendix has been attributed to William Oughtred,<ref name=Cajori /> who used the same symbol in his 1631 algebra text, {{#invoke:Lang|lang}}, stating:

Multiplication of species [i.e. unknowns] connects both proposed magnitudes with the symbol 'in' or Template:Char: or ordinarily without the symbol if the magnitudes be denoted with one letter.<ref>Template:Cite book</ref>

Other works have been identified in which crossed diagonals appear in diagrams involving multiplied numbers, such as Robert Recorde's The Ground of Arts<ref>Template:Cite book</ref>Template:Refn and Oswald Schreckenfuchs's 1551 edition of Almagest, but these are not symbolizations.<ref name="Cajori">Template:Cite book</ref>

Uses

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

• Multiplication of two numbers, where it is read as "times" or "multiplied by"<ref name=":1" />
• Cross product of two vectors, where it is usually read as "cross"
• Cartesian product of two sets, where it is usually read as "cross"<ref>{{#invoke:citation/CS1|citation

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• 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 datesTemplate:Snd for example 1225 and 1232Template:Snd the expression "1225×1232" means "no earlier than 1225 and no later than 1232".<ref>Template:Citation</ref>

A monadic Template:Char symbol is used by the APL programming language to denote the sign function.

Similar notations

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The lower-case Latin letter Template:Char 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: "Template:Mvar multiplied by Template:Mvar" can be written as Template:Math or Template:Math.<ref name=":1" />

Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the common variable Template:Mvar. In some countries, such as Germany, the primary symbol for multiplication is the "dot operator" Template:Char (as in Template:Math). This symbol is also used in compound units of measurement, e.g., N⋅m (see Template:Slink). In algebra, it is a notation to resolve ambiguity (for instance, "Template:Math times Template:Math" may be written as Template:Math, to avoid being confused with a value called Template:Math). This notation is used wherever multiplication should be written explicitly, such as in "Template:Math for Template:Math"; this usage is also seen in English-language texts. In some languages, the use of full stop as a multiplication symbol, such as Template:Math, is common when the symbol for decimal point is comma.

Historically, computer language syntax was restricted to the ASCII character set, and the asterisk Template: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 Template:Key press, Template:Key press, Template:Key press and Template:Key press, respectively.

Typing the character

HTML, SGML, XML	× or ×
macOS	citation	CitationClass=web }}</ref>
Microsoft Windows	Via the Emoji and Symbol input panel, invoked with the Template:Key press key combination (Windows 10 version 1803 and later) Via the Touch Keyboard component of the Taskbar (Windows 10 and later) Some non-English keyboard layouts have it as an explicit keytop, like in Arabic keyboard. Using US International keyboard layout, use Template:Key press Via the Character Map utility: in the eighth row, or by searching The Template:Key pressTemplate:Key pressTemplate:Key pressTemplate:Key press key combination using the numeric keypad<ref>{{#invoke:citation/CS1|citation	CitationClass=web }}</ref>
OpenOffice.org	times
TeX	\times \cdot
Unix-like (Linux, ChromeOS)	Template:KeypressTemplate:Keypress Template:Keypress Template:Keypress (UK extended layout)

Unicode and HTML entities

• Template:Unichar

Other variants and related characters:

• Template:Unichar
• Template:Unichar
• Template:Unichar (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 <U+2062> x )
• Template:Unichar (the interpunct, may be easier to type than the dot operator)
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar (intended to explicitly denote the cross product of two vectors)
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar
• Template:Unichar

See also

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

External links

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