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Multiplication sign

 

Multiplication sign

×
Multiplication sign

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 1
  • History 2
  • Similar notations 3
  • In computer software 4
  • Unicode 5
  • See also 6
  • References 7
  • External links 8

Uses

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

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

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 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

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
  • Alt Gr+
  • Alt+0215
  • Alt+0D7[8]
Unix-like
OpenOffice.org times
TeX \times
Unicode U+00D7

Unicode

  • 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

References

  1. ^ Stallings, L. (2000). "A Brief History of Algebraic Notation". School Science and Mathematics 100 (5): 230–235.  
  2. ^ "into, prep. and adj.",  
  3. ^ New Hart's rules: the handbook of style for writers and editors, Oxford University Press, 2005, p. 183,  
  4. ^ Florian Cajori (1919). A History of Mathematics. Macmillan. 
  5. ^ Stallings, L. (2000). "A Brief History of Algebraic Notation". School Science and Mathematics 100 (5): 230–235.  
  6. ^ http://www.apple.com/de/pro/tips/specialchar.html Apple Sonderzeichen (German / Deutsch)
  7. ^ http://www.typografie.info/typowiki/Mac_Zeichenpalette
  8. ^ http://www.fileformat.info/info/unicode/char/00D7/index.htm

External links

  • 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)
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