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Multiplication sign
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Image:Multiplication
The multiplication sign or times sign is the symbol ×. The symbol is similar to the lowercase letter x but is a more symmetric saltire, and has different uses. It is also known as St. Andrew's Cross[1] and dimension sign, or into sign.
Contents
Uses[edit]
In mathematics, the symbol × (read as times or multiplied by or into[2]) is primarily used to denote the
- Multiplication of two numbers
- Cross product of two vectors
- Cartesian product of two sets
- 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" (for example: "10 feet by 12 feet")
- Dimensions of a matrix
In biology, the multiplication sign is used in a botanical hybrid name, where it is read as "cross".
The multiplication sign is also used by historians for an event between two dates. When employed between two dates, for example 1225 and 1232, 1225×1232 means "no earlier than 1225 and no later than 1232". It can also be used in a date range: 1225×1232–1278.[3]
History[edit]
The × symbol for multiplication was introduced by William Oughtred in 1631.[4] It was chosen for religious reasons to represent the cross.[5]
Similar notations[edit]
The letter "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 a confusion: "a multiplied by b" can be written as ab or a b.
Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the commonly used variable x. In many non-Anglophone countries, rather than ×, the primary symbol for multiplication is U+22C5 ⋅ dot operator, for which the interpunct · may be substituted as a more accessible character. This symbol is also used in mathematics wherever multiplication should be written explicitly, such as in "ab = a⋅2 for b = 2"; this usage is also seen in English-language texts. In some languages (especially, French[citation needed] and Bulgarian) the use of full stop as a multiplication symbol, such as a.b, is common.
In programming languages, the standard notation of multiplication operator is U+002A * asterisk due to traditional restriction of all syntax of computer languages to the ASCII character repertoire.
In computer software[edit]
The × symbol is listed in the Latin-1 Supplement character set and is U+00D7 × multiplication sign (HTML × · ×) in Unicode. It can be invoked in various operating systems as per the table below.
The × symbol is used by the APL programming language to denote the sign function.
There is a similar character ⨯ at U+2A2F, but this is not always considered identical to U+00D7, as U+2A2F is intended to explicitly denote the cross product of two vectors.
| Mac OS X | in Character Palette, search for MULTIPLICATION SIGN[6][7] |
| HTML, SGML, XML | × and × |
| Microsoft Windows |
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| Unix-like |
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| OpenOffice.org | times |
| TeX | \times |
| Unicode | U+00D7 |
Unicode[edit]
- In Unicode, the basic character is U+00D7 × multiplication sign (HTML
×·×)
Other variants are encoded:
- U+2297 ⊗ circled times (HTML
⊗·⊗) - U+2715 ✕ multiplication x (HTML
✕) - U+2716 ✖ heavy multiplication x (HTML
✖) - U+2A09 ⨉ n-ary times operator (HTML
⨉) - U+2A2F ⨯ vector or cross product (HTML
⨯) - U+2A30 ⨰ multiplication sign with dot above (HTML
⨰) - U+2A31 ⨱ multiplication sign with underbar (HTML
⨱) - U+2A34 ⨴ multiplication sign in left half circle (HTML
⨴) - U+2A35 ⨵ multiplication sign in right half circle (HTML
⨵) - U+2A36 ⨶ circled multiplication sign with circumflex accent (HTML
⨶) - U+2A37 ⨷ multiplication sign in double circle (HTML
⨷) - U+2A3B ⨻ multiplication sign in triangle (HTML
⨻) - U+2AC1 ⫁ subset with multiplication sign below (HTML
⫁) - U+2AC2 ⫂ superset with multiplication sign below (HTML
⫂)
See also[edit]
References[edit]
- ^ Stallings, L. (2000). "A Brief History of Algebraic Notation". School Science and Mathematics 100 (5): 230–235. doi:10.1111/j.1949-8594.2000.tb17262.x. ISSN 0036-6803.
- ^ "into, prep. and adj.", Oxford English Dictionary Online (Oxford University Press), retrieved 2014-05-07
- ^ New Hart's rules: the handbook of style for writers and editors, Oxford University Press, 2005, p. 183, ISBN 978-0-19-861041-0
- ^ Florian Cajori (1919). A History of Mathematics. Macmillan.
- ^ Stallings, L. (2000). "A Brief History of Algebraic Notation". School Science and Mathematics 100 (5): 230–235. doi:10.1111/j.1949-8594.2000.tb17262.x. ISSN 0036-6803.
- ^ http://www.apple.com/de/pro/tips/specialchar.html Apple Sonderzeichen (German / Deutsch)
- ^ http://www.typografie.info/typowiki/index.php?title=Mac_Zeichenpalette
- ^ http://www.fileformat.info/info/unicode/char/00D7/index.htm
External links[edit]
- http://www.eki.ee/letter/chardata.cgi?ucode=00D7
- http://www.fileformat.info/info/unicode/char/00d7/index.htm (the general multiplication sign)
- http://www.fileformat.info/info/unicode/char/2a2f/index.htm (the cross product sign)