Modern Arabic mathematical notation is a mathematical notation based on the

Arabic script The Arabic script is the writing system used for Arabic and several other languages of Asia and Africa. It is the second-most widely used writing system in the world by number of countries using it or a script directly derived from it, and the ...

, 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 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 Latin alphabet 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 The Arabic script has numerous diacritics, which include: consonant pointing known as (), and supplementary diacritics known as (). The latter include the vowel marks termed (; singular: , '). The Arabic script is a modified abjad, where sh ...

'') 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 ...

. 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 univer ...

, 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" (sometimes called European) are used in western Arabic regions (e.g. Morocco) *" Eastern Arabic numerals" are used in middle and eastern Arabic regions (e.g. Egypt 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 speaking regions (e.g. Iran, Pakistan, India) 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 and the thousands separator 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; Walte ...

''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'' (al ...

Sets and number systems

Arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th c ...
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 a ...

Trigonometric and hyperbolic functions

Trigonometric functions

Hyperbolic functions

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

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

-1

in Latin-based notation.

Inverse hyperbolic functions

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. Mathematical notation Arabic, modern