Obelus
Encyclopedia
An obelus is a symbol consisting of a short horizontal line with a dot above and below. It is mainly used to represent the mathematical operation of division
. It is therefore commonly referred to as the division sign.
word for a sharpened stick, spit, or pointed pillar. This is the same root as that of the word "obelisk
". Originally this sign (or a plain line) was used in ancient manuscripts to mark passages
that were suspected of being corrupted or spurious.
The obelus was first used as a symbol for division in 1659 in the algebra
book Teutsche Algebra by Johann Rahn
. Some think that John Pell
, who edited the book, may have been responsible for this use of the symbol. The obelus had been used by some writers to represent subtraction, and that usage continued in some parts of Europe (including Norway
and, until fairly recently, Denmark
). Unicode
has a related character, ⁒, called "commercial minus sign", located at U+2052 (HTML ⁒).
typography to represent ranges (such as the range 1÷10), although this usage has been mostly discontinued. As of 2007, it was also used to indicate a range in Italian
documents (for example, 40% ÷ 50% would indicate 40 percent to 50 percent).
The obelus is primarily used as a symbol for division (as on a calculator
) and as an operator in elementary arithmetic
. Division is also signified in other ways — usually as a fraction
: by writing the operands one above the other and separated by a line, or on the same line separated by a solidus
or slash
.
In many non-Anglophone countries, the colon
is used as a division sign: “a divided by b” is written as a : b, and this is widely used to indicate a ratio
.
In Microsoft Windows
, the obelus is produced with Alt
+0247 or Alt
+246 on the number pad. In Mac OS
, it is produced with Option
+ / (Option + slash).
On UNIX-based systems using Screen
or X with a Compose key
enabled, it can be produced by composing : (colon) and - (minus), though this is locale- and setting-dependent. It may also be input by Unicode code-point on GTK-based applications by pressing Control + Shift + U, followed by the codepoint in hexadecimal (F7) and terminated by return.
In the Unicode
character set, the obelus is known as the “division sign” and has the code point U+00F7. In HTML
, it can be encoded
as ÷ or ÷ (at HTML level 3.2), or as ÷.
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
. It is therefore commonly referred to as the division sign.
History
The word "obelus" comes from the GreekGreek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
word for a sharpened stick, spit, or pointed pillar. This is the same root as that of the word "obelisk
Obelisk
An obelisk is a tall, four-sided, narrow tapering monument which ends in a pyramid-like shape at the top, and is said to resemble a petrified ray of the sun-disk. A pair of obelisks usually stood in front of a pylon...
". Originally this sign (or a plain line) was used in ancient manuscripts to mark passages
Obelism
Obelism is the practice of annotating manuscripts with marks set in the margins. Modern obelisms are used by editors when blue-penciling a manuscript or typescript...
that were suspected of being corrupted or spurious.
The obelus, invented by Aristarchus to mark suspected passages in Homer, is frequent in MSS. [i.e. manuscriptManuscriptA manuscript or handwrite is written information that has been manually created by someone or some people, such as a hand-written letter, as opposed to being printed or reproduced some other way...
s] of the Gospel to mark just those sections, like the Pericope in John, which modern editors reject. The first corrector of א, probably the contemporary διορθωτής, was at pains to enclose in brackets and mark with dots for deletion two famous passages in Luke written by the original scribe which, being absent from B W 579 and the Egyptian versions, we infer were not accepted in the text at that time dominant in Alexandria, viz. the incident of the "Bloody Sweat" in Gethsemane (Lk.xxi.43 f.) and the saying "Father forgive them" (Lk.xi.34).
The obelus was first used as a symbol for division in 1659 in the algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
book Teutsche Algebra by Johann Rahn
Johann Rahn
Johann Rahn was a Swiss mathematician who is credited with the first use of the division symbol, ÷ and the therefore sign, ∴. The symbol is used in Teutsche Algebra, published in 1659.-References:...
. Some think that John Pell
John Pell
-Early life:He was born at Southwick in Sussex. He was educated at Steyning Grammar School, and entered Trinity College, Cambridge, at the age of thirteen. During his university career he became an accomplished linguist, and even before he took his B.A. degree corresponded with Henry Briggs and...
, who edited the book, may have been responsible for this use of the symbol. The obelus had been used by some writers to represent subtraction, and that usage continued in some parts of Europe (including Norway
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...
and, until fairly recently, Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
). Unicode
Unicode
Unicode is a computing industry standard for the consistent encoding, representation and handling of text expressed in most of the world's writing systems...
has a related character, ⁒, called "commercial minus sign", located at U+2052 (HTML ⁒).
Uses
The obelus was used occasionally in Polish languagePolish language
Polish is a language of the Lechitic subgroup of West Slavic languages, used throughout Poland and by Polish minorities in other countries...
typography to represent ranges (such as the range 1÷10), although this usage has been mostly discontinued. As of 2007, it was also used to indicate a range in Italian
Italian language
Italian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
documents (for example, 40% ÷ 50% would indicate 40 percent to 50 percent).
The obelus is primarily used as a symbol for division (as on a calculator
Calculator
An electronic calculator is a small, portable, usually inexpensive electronic device used to perform the basic operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.The first solid-state electronic...
) and as an operator in elementary arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
. Division is also signified in other ways — usually as a fraction
Fraction (mathematics)
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...
: by writing the operands one above the other and separated by a line, or on the same line separated by a solidus
Solidus (punctuation)
The solidus is a punctuation mark used to indicate fractions including fractional currency. It may also be called a shilling mark, an in-line fraction bar, or a fraction slash....
or slash
Slash (punctuation)
The slash is a sign used as a punctuation mark and for various other purposes. It is now often called a forward slash , and many other alternative names.-History:...
.
In many non-Anglophone countries, the colon
Colon (punctuation)
The colon is a punctuation mark consisting of two equally sized dots centered on the same vertical line.-Usage:A colon informs the reader that what follows the mark proves, explains, or lists elements of what preceded the mark....
is used as a division sign: “a divided by b” is written as a : b, and this is widely used to indicate a ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
.
In Microsoft Windows
Microsoft Windows
Microsoft Windows is a series of operating systems produced by Microsoft.Microsoft introduced an operating environment named Windows on November 20, 1985 as an add-on to MS-DOS in response to the growing interest in graphical user interfaces . Microsoft Windows came to dominate the world's personal...
, the obelus is produced with Alt
Alt key
The Alt key on a computer keyboard is used to change the function of other pressed keys. Thus, the Alt key is a modifier key, used in a similar fashion to the Shift key. For example, simply pressing "A" will type the letter a, but if you hold down either Alt key while pressing A, the computer...
+0247 or Alt
Alt key
The Alt key on a computer keyboard is used to change the function of other pressed keys. Thus, the Alt key is a modifier key, used in a similar fashion to the Shift key. For example, simply pressing "A" will type the letter a, but if you hold down either Alt key while pressing A, the computer...
+246 on the number pad. In Mac OS
Mac OS
Mac OS is a series of graphical user interface-based operating systems developed by Apple Inc. for their Macintosh line of computer systems. The Macintosh user experience is credited with popularizing the graphical user interface...
, it is produced with Option
Option key
The Option key is a modifier key present on Apple keyboards. It is located between the Control key and Command key on a typical Mac keyboard. There are two option keys on modern Mac desktop and notebook keyboards, one on each side of the space bar....
+ / (Option + slash).
On UNIX-based systems using Screen
GNU Screen
GNU Screen is a software application that can be used to multiplex several virtual consoles, allowing a user to access multiple separate terminal sessions inside a single terminal window or remote terminal session...
or X with a Compose key
Compose key
A compose key, available on some computer keyboards, is a special kind of modifier key designated to signal the software to interpret the following sequence of two keystrokes as a combination in order to produce a character not found directly on the keyboard...
enabled, it can be produced by composing : (colon) and - (minus), though this is locale- and setting-dependent. It may also be input by Unicode code-point on GTK-based applications by pressing Control + Shift + U, followed by the codepoint in hexadecimal (F7) and terminated by return.
In the Unicode
Unicode
Unicode is a computing industry standard for the consistent encoding, representation and handling of text expressed in most of the world's writing systems...
character set, the obelus is known as the “division sign” and has the code point U+00F7. In HTML
HTML
HyperText Markup Language is the predominant markup language for web pages. HTML elements are the basic building-blocks of webpages....
, it can be encoded
Character encodings in HTML
HTML has been in use since 1991, but HTML 4.0 was the first standardized version where international characters were given reasonably complete treatment...
as ÷ or ÷ (at HTML level 3.2), or as ÷.