Multiplication sign
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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">Template:Cite 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 Template: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, Template: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>Template:Cite web</ref>
- 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")
- Display 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
The lower-case Latin letter Template:Char is sometimes used in place of the multiplication sign. This is considered incorrect in mathematical writing.Template:Cn
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.
Unicode and HTML entities
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
- Template:Anli (a general guide to entering "off-keyboard" symbols).
- Template:Anli