Modern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university 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.
Notation differs slightly from region to another. In tertiary education, most regions use the Western notation. The notation mainly differs in numeral system used, and in mathematical symbol used.
There are three numeral systems used in right to left mathematical notation.
European (descended from Western Arabic) |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Arabic-Indic (Eastern Arabic) | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? |
Perso-Arabic variant | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? |
Urdu variant |
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.
Sometimes, symbols used in Arabic mathematical notation differ according to the region:
Sometimes, mirrored Latin symbols are used in Arabic mathematical notation (especially in western Arabic regions):
However, in Iran, usually Latin symbols are used.
Latin | Arabic | Notes | |
---|---|---|---|
? | From the Arabic letter ? ?alif; a and ? ?alif are the first letters of the Latin alphabet and the Arabic alphabet's ?abjad? sequence respectively | ||
? | A dotless ? b; b and ? b are the second letters of the Latin alphabet and the ?abjad? sequence respectively | ||
| From the initial form of ? , or that of a dotless ? j?m; c and ? j?m are the third letters of the Latin alphabet and the ?abjad? sequence respectively | ||
? | From the Arabic letter ? d?l; d and ? d?l are the fourth letters of the Latin alphabet and the ?abjad? sequence respectively | ||
? | From the Arabic letter ? s?n. It is contested that the usage of Latin x in maths is derived from the first letter ? n (without its dots) of the Arabic word ?ay?(un) [?aj?(un)], meaning thing.^{[1]} (X was used in old Spanish for the sound /?/). However, according to others there is no historical evidence for this.^{[2]}^{[3]} | ||
? | From the Arabic letter ? d | ||
? | From the Arabic letter ? ?ayn |
Description | Latin | Arabic | Notes | |
---|---|---|---|---|
Euler's number | ? | Initial form of the Arabic letter ? h. Both Latin letter e and Arabic letter ? h are descendants of Phoenician letter h?. | ||
imaginary unit | ? | From ? t, which is in turn derived from the first letter of the second word of ? wa?da?un taliyya "imaginary unit" | ||
pi | ? | From ? ; also in some regions | ||
radius | | From ? n?n followed by a dotless ? q?f, which is in turn derived from nu?fu l-qu?r "radius" | ||
kilogram | kg | | From k?f-j?m-m?m. In some regions alternative symbols like ( k?f-?ayn) or ( k?f-l?m-?ayn) are used. All three abbreviations are derived from k?lr?m "kilogram" and its variant spellings. | |
gram | g | | From j?m-m?m, which is in turn derived from ? jr?m, a variant spelling of ? ?r?m "gram" | |
meter | m | ? | From ? m?m, which is in turn derived from mitr "meter" | |
centimeter | cm | | From s?n-m?m, which is in turn derived from ? "centimeter" | |
millimeter | mm | | From m?m-m?m, which is in turn derived from mill?mitr "millimeter" | |
kilometer | km | | From k?f-m?m; also ( k?f-l?m-m?m) in some regions; both are derived from ? k?l?mitr "kilometer". | |
second | s | ? | From ? , which is in turn derived from niya "second" | |
minute | min | ? | From ? d?l?, which is in turn derived from daq?qa "minute"; also ( ? , i.e. dotless ? q?f) in some regions | |
hour | h | ? | From ? s?n?, which is in turn derived from ? sa "hour" | |
kilometer per hour | km/h | /? | From the symbols for kilometer and hour | |
degree Celsius | °C | °? | From ? s?n, which is in turn derived from the second word of ? ? darajat s?lss "degree Celsius"; also ( °? ) from ? m?m?, which is in turn derived from the first letter of the third word of ? "degree centigrade" | |
degree Fahrenheit | °F | °? | From ? f, which is in turn derived from the second word of ? darajat fahranh?yt "degree Fahrenheit" | |
millimeters of mercury | mmHg | ? | From ? m?m-m?m zayn, which is in turn derived from the initial letters of the words ? "millimeters of mercury" | |
Ångström | Å | | From ?alif with hamzah and ring above, which is in turn derived from the first letter of "Ångström", variously spelled or |
Description | Latin | Arabic | Notes | |
---|---|---|---|---|
Natural numbers | ? | From ? , which is in turn derived from the first letter of the second word of ?adadun ?abiyyun "natural number" | ||
Integers | ? | From ? d, which is in turn derived from the first letter of the second word of ? ?adadun ?aun "integer" | ||
Rational numbers | ? | From ? n?n, which is in turn derived from the first letter of ? nisba "ratio" | ||
Real numbers | ? | From ? , which is in turn derived from the first letter of the second word of ?adadun ?aq?qiyyun "real number" | ||
Imaginary numbers | ? | From ? t, which is in turn derived from the first letter of the second word of ?adadun taliyyun "imaginary number" | ||
Complex numbers | ? | From ? m?m, which is in turn derived from the first letter of the second word of ? ?adadun markabun "complex number" | ||
Empty set | ? | |||
Is an element of | ? | A mirrored ? | ||
Subset | ? | A mirrored ? | ||
Superset | ? | A mirrored ? | ||
Universal set | ? | From ? n, which is in turn derived from the first letter of the second word of majmatun mila "universal set" |
Description | Latin | Arabic | Notes | |
---|---|---|---|---|
Percent | % | ? | e.g. 100% "?" | |
Permille | ? | ? | ? is an Arabic equivalent of the per ten thousand sign ?. | |
Is proportional to | ? | A mirrored ? | ||
n ^{th} root | ^{?}? | ? is a dotless ? n?n while ? is a mirrored radical sign ? | ||
Logarithm | | From l?m-w?w, which is in turn derived from lr?tm "logarithm" | ||
Logarithm to base b | _{?} | |||
Natural logarithm | _{?} | From the symbols of logarithm and Euler's number | ||
Summation | | m?m-medial form of j?m is derived from the first two letters of majm "sum"; also (?, a mirrored summation sign ?) in some regions | ||
Product | | From j?m-l. The Arabic word for "product" is ? jadun. Also in some regions. | ||
Factorial | ? | Also ( ?! ) in some regions | ||
Permutations | ^{?}?_{?} | Also ( ?( ?) ) is used in some regions as | ||
Combinations | ^{?}?_{?} | Also ( ?( ?) ) is used in some regions as and (^{?} _{?} ) as the binomial coefficient |
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 is added to the end of trigonometric functions in Latin-based notation.
Description | Hyperbolic sine | Hyperbolic cosine | Hyperbolic tangent | Hyperbolic cotangent | Hyperbolic secant | Hyperbolic cosecant |
---|---|---|---|---|---|---|
Latin | ||||||
Arabic | | ? | | ? | | ? |
For inverse trigonometric functions, the superscript -? in Arabic notation is similar in usage to the superscript in Latin-based notation.
Description | Inverse sine | Inverse cosine | Inverse tangent | Inverse cotangent | Inverse secant | Inverse cosecant |
---|---|---|---|---|---|---|
Latin | ||||||
Arabic | ^{-?} | ^{-?} | ^{-?} | ^{-?} | ^{-?} | ^{-?} |
Description | Latin | Arabic | Notes | |
---|---|---|---|---|
Limit | ? | ? n?n-h-?alif is derived from the first three letters of Arabic nih?ya "limit" | ||
function | ?(?) | ? d?l is derived from the first letter of ? "function". Also called ?, for short, in some regions. | ||
derivatives | ?`(?)? ??/ ?? ? ?^{?}?/ ??^{?} ? ??/?? | ` is a mirrored prime ? while ? is an Arabic comma. The ? signs should be mirrored: ?. | ||
Integrals | ? ?? ?? ?? | Mirrored ?, ?, ? and ? |
Nor is there historical evidence to support the statement found in Noah Webster's Dictionary, under the letter x, to the effect that 'x was used as an abbreviation of Ar. shei (a thing), something, which, in the Middle Ages, was used to designate the unknown, and was then prevailingly transcribed as xei.'
There is no evidence in support of the hypothesis that x is derived ultimately from the mediaeval transliteration xei of shei "thing", used by the Arabs to denote the unknown quantity, or from the compendium for L. res "thing" or radix "root" (resembling a loosely-written x), used by mediaeval mathematicians.