Multiplication sign

Today, Multiplication sign is a topic that has gained relevance in different areas of society. From politics and economics to culture and technology, Multiplication sign has become a point of interest that generates debate and reflection. Over time, the impact of Multiplication sign has increased, directly or indirectly affecting a wide spectrum of the population. In this article, we will explore the different facets of Multiplication sign and analyze its influence on contemporary reality, as well as the possible implications it has for the future.

"×" redirects here. Not to be confused with the letter X.
×
Multiplication sign
In UnicodeU+00D7 × MULTIPLICATION SIGN (×)
Different from
Different fromU+0078 x LATIN SMALL LETTER X
Related
See alsoU+22C5 ⋅ DOT OPERATOR
U+00F7 ÷ DIVISION SIGN

The multiplication sign (×), 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 × is similar to a lowercase X (x).

History

The earliest known use of the × symbol to indicate multiplication appears in an anonymous appendix to the 1618 edition of John Napier's Mirifici Logarithmorum Canonis Descriptio.[3] This appendix has been attributed to William Oughtred,[3] who used the same symbol in his 1631 algebra text, Clavis Mathematicae, stating:

Multiplication of species connects both proposed magnitudes with the symbol 'in' or ×: 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][6] 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"[7]
  • 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 dates – for example 1225 and 1232 – the expression "1225×1232" means "no earlier than 1225 and no later than 1232".[8]

A monadic × symbol is used by the APL programming language to denote the sign function.

Similar notations

Main article: Multiplication: Notation

The lower-case Latin 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 confusion: "a multiplied by b" can be written as ab or a b.[1]

Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the common variable x. In some countries, such as Germany, the primary symbol for multiplication is the "dot operator" ⋅ (as in a⋅b). This symbol is also used in compound units of measurement, e.g., N⋅m (see International System of Units § Lexicographic conventions). In algebra, it is a notation to resolve ambiguity (for instance, "b times 2" may be written as b⋅2, to avoid being confused with a value called b2). This notation is used 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, the use of full stop as a multiplication symbol, such as a.b, is common when the symbol for decimal point is comma.

Historically, computer language syntax was restricted to the ASCII character set, and the asterisk * 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 +, -, * and /, respectively.

Typing the character

HTML, SGML, XML × or ×
macOS In the Character Palette by searching for MULTIPLICATION SIGN[9]
Microsoft Windows
  • Via the Emoji and Symbol input panel, invoked with the ⊞ Win+. 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 Alt+=
  • Via the Character Map utility: in the eighth row, or by searching
  • The Alt+0215 key combination using the numeric keypad[10]
OpenOffice.org times
TeX
  • \times
  • \cdot
Unix-like (Linux, ChromeOS)

Unicode and HTML entities

  • U+00D7 × MULTIPLICATION SIGN (×)

Other variants and related characters:

  • U+002A * ASTERISK (*, *)
  • U+2217 ∗ ASTERISK OPERATOR (∗)
  • U+2062 INVISIBLE TIMES (&InvisibleTimes;, &it;) (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 )
  • U+00B7 · MIDDLE DOT (&middot;, &CenterDot;, &centerdot;) (the interpunct, may be easier to type than the dot operator)
  • U+2297 ⊗ CIRCLED TIMES (&CircleTimes;, &otimes;)
  • U+22C5 ⋅ DOT OPERATOR (&sdot;)
  • U+2715 ✕ MULTIPLICATION X
  • U+2716 ✖ HEAVY MULTIPLICATION X
  • U+2A09 ⨉ N-ARY TIMES OPERATOR
  • U+2A2F ⨯ VECTOR OR CROSS PRODUCT (&Cross;) (intended to explicitly denote the cross product of two vectors)
  • U+2A30 ⨰ MULTIPLICATION SIGN WITH DOT ABOVE (&timesd;)
  • U+2A31 ⨱ MULTIPLICATION SIGN WITH UNDERBAR (&timesbar;)
  • U+2A34 ⨴ MULTIPLICATION SIGN IN LEFT HALF CIRCLE (&lotimes;)
  • U+2A35 ⨵ MULTIPLICATION SIGN IN RIGHT HALF CIRCLE (&rotimes;)
  • U+2A36 ⨶ CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENT (&otimesas;)
  • U+2A37 ⨷ MULTIPLICATION SIGN IN DOUBLE CIRCLE (&Otimes;)
  • U+2A3B ⨻ MULTIPLICATION SIGN IN TRIANGLE (&tritime;)
  • U+2AC1 ⫁ SUBSET WITH MULTIPLICATION SIGN BELOW (&submult;)
  • U+2AC2 ⫂ SUPERSET WITH MULTIPLICATION SIGN BELOW (&supmult;)

See also

References

  1. ^ a b c Weisstein, Eric W. "Multiplication". mathworld.wolfram.com. Retrieved 2020-08-26.
  2. ^ 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.
  3. ^ a b c Cajori, Florian (1928). A History of Mathematical Notations, Volume I: Notations in Elementary Mathematics. Open Court. pp. 251–252.
  4. ^ William Oughtred (1667). Clavis Mathematicae. p. 10. Multiplicatio speciosa connectit utramque magintudinem propositam cum notâ in vel ×: vel plerumque absque notâ, si magnitudines denotentur unica litera
  5. ^ Recorde, Robert (1618). The Ground of Arts. London: John Beale.
  6. ^ The diagonals do not appear in the original 1543 edition, leaving their priority to Oughtred uncertain.
  7. ^ Nykamp, Duane. "Cartesian product definition". Math Insight. Retrieved August 26, 2020.
  8. ^ New Hart's rules: the handbook of style for writers and editors, Oxford University Press, 2005, p. 183, ISBN 978-0-19-861041-0
  9. ^ "Mac Zeichenpalette" (in German). TypoWiki. Archived from the original on 2007-10-25. Retrieved 2009-10-09.
  10. ^ "Unicode Character 'MULTIPLICATION SIGN' (U+00D7)". Fileformat.info. Retrieved 2017-01-13.