Modern Arabic mathematical notation is a

mathematical notation Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathem ...

based on the Arabic script, used especially at

pre-university According to the International Standard Classification of Education (ISCED), basic education comprises the two stages primary education and lower secondary education. Universal basic education Basic education featured heavily in the 1997 ISCED ...

levels of education. Its form is mostly derived from Western notation, but has some notable features that set it apart from its Western counterpart. The most remarkable of those features is the fact that it is written from right to left following the normal direction of the Arabic script. Other differences include the replacement of the

Latin alphabet The Latin alphabet or Roman alphabet is the collection of letters originally used by the ancient Romans to write the Latin language. Largely unaltered with the exception of extensions (such as diacritics), it used to write English and th ...

letters for symbols with Arabic letters and the use of Arabic names for functions and relations.

Features

*It is written from right to left following the normal direction of the Arabic script. Other differences include the replacement of the

letters for symbols with Arabic letters and the use of Arabic names for functions and relations. *The notation exhibits one of the very few remaining vestiges of non-dotted Arabic scripts, as dots over and under letters ('' i'jam'') are usually omitted. *Letter cursivity (connectedness) of Arabic is also taken advantage of, in a few cases, to define variables using more than one letter. The most widespread example of this kind of usage is the canonical symbol for the radius of a circle (), which is written using the two letters nūn and

qāf Qoph ( Phoenician Qōp ) is the nineteenth letter of the Semitic scripts. Aramaic Qop is derived from the Phoenician letter, and derivations from Aramaic include Hebrew Qof , Syriac Qōp̄ ܩ and Arabic . Its original sound value was a W ...

. When variable names are juxtaposed (as when expressing multiplication) they are written non-cursively.

Variations

Notation differs slightly from region to another. In

tertiary education Tertiary education, also referred to as third-level, third-stage or post-secondary education, is the educational level following the completion of secondary education. The World Bank, for example, defines tertiary education as including univers ...

, most regions use the Western notation. The notation mainly differs in numeral system used, and in mathematical symbol used.

Numeral systems

There are three numeral systems used in right to left mathematical notation. *"

Western Arabic numerals Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers such as ...

" (sometimes called European) are used in western Arabic regions (e.g.

Morocco Morocco (),, ) officially the Kingdom of Morocco, is the westernmost country in the Maghreb region of North Africa. It overlooks the Mediterranean Sea to the north and the Atlantic Ocean to the west, and has land borders with Algeria t ...

) *"

Eastern Arabic numerals The Eastern Arabic numerals, also called Arabic-Hindu numerals or Indo–Arabic numerals, are the symbols used to represent numerical digits in conjunction with the Arabic alphabet in the countries of the Mashriq (the east of the Arab world) ...

" are used in middle and eastern Arabic regions (e.g.

Egypt Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and southwest corner of Asia via a land bridge formed by the Sinai Peninsula. It is bordered by the Medit ...

and Syria) *"Eastern Arabic-Indic numerals" are used in

Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, the majority ethnic group in Iran, not to be conflated with the Iranic peoples ** Persian language, an Iranian language of the ...

and

Urdu Urdu (;"Urdu"
'' Iran Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...

Pakistan Pakistan ( ur, ), officially the Islamic Republic of Pakistan ( ur, , label=none), is a country in South Asia. It is the world's fifth-most populous country, with a population of almost 243 million people, and has the world's second-lar ...

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

) Written numerals are arranged with their lowest-value digit to the right, with higher value positions added to the left. That is identical to the arrangement used by Western texts using Hindu-Arabic numerals even though Arabic script is read from right to left. The symbols "٫" and "٬" may be used as the

decimal mark A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choi ...

and the

thousands separator A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The choi ...

respectively when writing with Eastern Arabic numerals, e.g. ''3.14159265358'', ''1,000,000,000''. Negative signs are written to the left of magnitudes, e.g. ''−3''. In-line fractions are written with the numerator and denominator on the left and right of the fraction slash respectively, e.g. ''2/7''.

Mirrored Latin symbols

Sometimes, symbols used in Arabic mathematical notation differ according to the region: * ''nūn''-''hāʾ''-''ʾalif'' is derived from the first three letters of

Arabic Arabic (, ' ; , ' or ) is a Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C. E.Watson; Walter ...

''nihāya'' "limit". * ''ḥadd'' is

for "limit". Sometimes, mirrored Latin symbols are used in Arabic mathematical notation (especially in western Arabic regions): * is derived from

''maǧmūʿ'' "sum". However, in Iran, usually Latin symbols are used.

Examples

Mathematical letters

Mathematical constants A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Const ...
and
units Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * Unit (album), ...

Sets and
number systems A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...

Arithmetic and
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

Trigonometric and hyperbolic functions

Trigonometric functions In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in al ...

Hyperbolic functions In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the un ...

The letter ( ''zayn'', from the first letter of the second word of "hyperbolic function") is added to the end of trigonometric functions to express hyperbolic functions. This is similar to the way

\operatorname

is added to the end of trigonometric functions in Latin-based notation.

Inverse trigonometric functions In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Spec ...

For inverse trigonometric functions, the superscript in Arabic notation is similar in usage to the superscript

-1

in Latin-based notation.

Inverse hyperbolic functions In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. Th ...

Calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

Complex analysis

References

{{Reflist

External links

Multilingual mathematical e-document processing

Arabic mathematical notation
- W3C Interest Group Note.
Arabic math editor
- by WIRIS.

Arabic, modern