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.[1]
The symbol is also used in botany, in botanical hybrid names.
The form is properly a four-fold rotationally symmetric saltire.[2] 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 Script error: No such module "Lang"..[3] This appendix has been attributed to William Oughtred,[3] who used the same symbol in his 1631 algebra text, Script error: No such module "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.[4]
Other works have been identified in which crossed diagonals appear in diagrams involving multiplied numbers, such as Robert Recorde's The Ground of Arts[5]Template:Refn and Oswald Schreckenfuchs's 1551 edition of Almagest, but these are not symbolizations.[3]
Uses
In mathematics, the symbol × has a number of uses, including
- Multiplication of two numbers, where it is read as "times" or "multiplied by"[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"[6]
- 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".[7]
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.Script error: No such module "Unsubst".
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 abScript error: No such module "Check for unknown parameters". or a bScript error: No such module "Check for unknown parameters"..[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 a⋅bScript error: No such module "Check for unknown parameters".). 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, "bScript error: No such module "Check for unknown parameters". times 2Script error: No such module "Check for unknown parameters"." may be written as b⋅2Script error: No such module "Check for unknown parameters"., to avoid being confused with a value called b2Script error: No such module "Check for unknown parameters".). This notation is used wherever multiplication should be written explicitly, such as in "ab = a⋅2Script error: No such module "Check for unknown parameters". for b = 2Script error: No such module "Check for unknown parameters"."; this usage is also seen in English-language texts. In some languages, the use of full stop as a multiplication symbol, such as a.bScript error: No such module "Check for unknown parameters"., 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 Script error: No such module "key"., Script error: No such module "key"., Script error: No such module "key". and Script error: No such module "key"., 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
References
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- ↑ a b c Script error: No such module "citation/CS1".
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- ↑ Script error: No such module "citation/CS1".
- ↑ Script error: No such module "citation/CS1".
- ↑ Script error: No such module "citation/CS1".
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External links
- Script error: No such module "citation/CS1".
- Script error: No such module "citation/CS1".
- Script error: No such module "citation/CS1".