Multiplication sign
The mark is a mathematical operator for multiplication.
- 6.1 encoding
- 6.2 keyboard
- 6.3 replacement by other characters
- 6.4 Similar and related marks
Typography
All typographical mark are seen centrally set and matched to the size and position of the digits in a font, and the other arithmetic operators. A substitution of the mark by others, similar characters (such as a small letter x or the simple asterisk *), the "correct" differently than the blank characters found on computer keyboards faster, but leads to a typographically less sophisticated typeface, especially since the asterisk in many fonts is superscript, because it is often used as a footnote mark.
Simple and advanced mathematics
Arithmetic
In the Grundrechenart multiplying the Malpunkt · and the cross × in content equivalent; the use is slightly different.
The cross × ( 215 Unicode, HTML times) is used
- If the multiplication must be represented visually striking about on a poster: 5 × 2 free tickets!
- If the factors Symbols and numbers are not, but words: Business tax = tax amount × multiplier
- If out of context length times width or width times height or width times height times depth be specified: Oil on canvas, 46.5 × 54.7 cm, Alte Nationalgalerie
- If only the left factor is specified, so in terms of times or times: Magnification: 6X
- In Anglo-American cultures influenced and in France in the classroom and everyday life.
The Malpunkt · ( 183 Unicode, HTML middot ) is used, however,
- If calculations are shown with symbols and numbers: a = 5 · x ² 7
- In Germany in the classroom.
In some cases, such as the multiplication of unit symbols, including a ( narrow ) space can be used as a mark, or the mark is omitted entirely (example: Nm Newton meter is a common, shorthand for N · m). In more scientific calculations Malpunkt is then entirely omitted if the design allows it and no likelihood of confusion.
In the source code of computer programs, the asterisk * (ASCII 42) is used.
Vector Analysis
For products of vectors, the result differs significantly by whether · or × are used; the torque M = F × s is quite different from the work W = F · s
Scalar product
For the join operation is scalar (English dot product ) is ( the Unicode character U 22 C5, HTML Entity: ⋅ ) a ⋅ provided. It would also allow for a substantive analysis of whether on both sides of ⋅ actually a vector is. Created Graphically, it is just like a · or something semi-bold; in normal font sizes, the two characters are visually almost indistinguishable.
If it with the newer ⋅ however, could be a display problem, can alternatively the · be used.
Were not written as a scientific work with mechanical typewriters or transmitted in ASCII character set, you had to distinguish alternatively, the simple point. need to use; this can be adjusted upon detection.
Cross product
For this join operation, there is currently - in contrast to the scalar product - no separate character; it is the cross × (Unicode U 00 D7, HTML Entity: × ) to use, so " cross product " next " vector product ".
Previously you had to dodge x here on the * or the letter if necessary.
Cartesian product
For the Cartesian product of the same applies as for the cross product.
Biology
The Mark Cross is also used in the names of species of hybrid crosses.
DIN 5008
DIN 5008 describes text processing in the office and administration area.
It is provided here as Malpunkt the centrally set point. The currently valid edition (May 2005) can alternatively even the "normal" set end - point. to, but this was deleted from the draft revision of November 2009.
For the time - cross of the lowercase letter x is provided. This has the background that mass-produced goods such as delivery notes and invoices must be prepared with the least possible time and cost, and for this the simple push of a button to meet on the x key. In particular cases, a document should be however designed particularly appealing and additional effort is required, the standard shall not prevent.
Besides, all arithmetic operators are basically enclose here in space, except or - act as sign of a number.
History of Symbols
The oldest symbol appears to be the Malkreuz ( × ). It was used for the first time by the English mathematician William Oughtred in his work Clavis Mathematicae, published in 1631 in London. Probably Oughtred used the Malkreuz since 1618, if an anonymous appendix comes to the English translation of John Napier's Descriptio of him. The derivation of the symbol - the letter (X ) or the St. Andrew's cross - is not clear.
The German scientist Gottfried Wilhelm Leibniz declined the Malkreuz off due to the likelihood of confusion with the letter X and preferred the dot ( · ). Leibniz used the multiplication point in an exchange of letters of the year 1698, but it has probably already been introduced in 1694 or earlier in his mathematical notation.
Johann Rahn introduced the asterisk (*) for multiplication. Together with the symbol of the division ( ÷ ) of these first appeared in his book Teutsche Algebra, published 1659th
Representation in computer systems
Coding
The character encoding of Unicode standard contains several multiplication sign. You are in the following positions:
In the U 2715 / 2716 be remembered, however, that they come from the section Dingbats and only decorative versions of the normal small cross U 00 D7; they have no special mathematical significance and are not to be used in normal text.
The signs referred to as " OPERATOR " belong to the higher mathematics and not arithmetic.
The " Invisible multiplication sign " is provided for this purpose, the individual factors to first disconnect semantically in coding in scientific typesetting. Then about a narrow space can be used in the desired width (see above) for the presentation.
In the ASCII character set from 1963, none of the characters is included, which is why many older computer systems they could not represent. The ASCII extensions to ISO 6937 in 1983 and ISO 8859-1 ( Latin 1) from 1986 already contained the Malkreuz.
Keyboard
On keyboards with the occupancy T2 accordance with the revised German standard DIN 2137:2012-06 is entered:
- The mark x with the key combination Alt Gr ^ ( caret at the top left button).
- · The center with the key sequence group change ⇨ followed by. ( Point).
In addition, conventional computer keyboards contain any of the above listed mark, syntactically and typographically correct. Instead, produce both the asterisk key in the main block of the keyboard and the numeric keypad Malzeichentaste in the simple asterisk (*; Unicode U 002 A), which usually leads to an unsatisfactory typeface. From almost all computer programs with calculating functions and also in almost all programming languages , the asterisk the correct mark on the other hand, however, is recognized as arithmetic operator for multiplication, often not.
On Linux computers with a German keyboard, the center · (U 00 B7) can be the key combination Alt Gr generated by simultaneously pressing the ⇧ Shift key to reach the mark × (U 00 D7). When using the Swiss keyboard layout ( German and French language variant), the center is located on the third assignment ( Alt ) key. and the mark on the fourth assignment ( Alt ⇧ Shift ) key.
Under Windows, the characters using the character table or the keyboard shortcuts can insert Alt 0183 for the center as well as Alt 0215 for the mark.
On Apple Macintosh computers, the characters can be found in the character palette using the appropriate name, for example MULTIPLICATION SIGN,.
With the Neo keyboard layout Malpunkt · by Mod3 × ( number pad) can be entered. The crosses × is on Mod4 × ( number pad).
Replacement by other characters
Because of the lack of the mark on the keyboard, the characters often by the letter x ( uppercase or lowercase) or the simple asterisk (* ) must be replaced. When using a sans serif font ( such as Arial ) is already the shape of the small x the mark pretty close, but it is of course still on the base line and off-center.