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 Greek and Latin alphabet letters for symbols with Arabic letters and the use of Arabic names for functions and relations.
Notation differs slightly from one region to another. In tertiary education, most regions use the Western notation. The notation mainly differs in numeral system used, and in mathematical symbols used.
There are three numeral systems used in right to left mathematical notation.
| European (descended from Western Arabic) | 4 | 9 | |||||||||
| Arabic-Indic (Eastern Arabic)< | -- U+0660 thru U+0669 --> | Arabic: ٠|italic=no | Arabic: ١|italic=no | Arabic: ٢|italic=no | Arabic: ٣|italic=no | Arabic: ٤|italic=no | Arabic: ٥|italic=no | Arabic: ٦|italic=no | Arabic: ٧|italic=no | Arabic: ٨|italic=no | Arabic: ٩|italic=no |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Perso-Arabic variant< | -- U+06F0 thru U+06F9 --> | Persian: ۰|italic=no | Persian: ۱|italic=no | Persian: ۲|italic=no | Persian: ۳|italic=no | Persian: ۴|italic=no | Persian: ۵|italic=no | Persian: ۶|italic=no | Persian: ۷|italic=no | Persian: ۸|italic=no | Persian: ۹|italic=no |
| Urdu variant |
Sometimes, symbols used in Arabic mathematical notation differ according to the region:
Sometimes, mirrored Latin and Greek symbols are used in Arabic mathematical notation (especially in western Arabic regions):
However, in Iran, usually Latin and Greek symbols are used.
| Latin | Arabic | Notes | |
|---|---|---|---|
a | From the Arabic letter Arabic: ا ʾalif; a and Arabic: ا ʾalif are the first letters of the Latin alphabet and the Arabic alphabet's ʾabjadī sequence respectively, and the letters also share a common ancestor and the same sound | ||
b | A dotless Arabic: ب bāʾ; b and Arabic: ب bāʾ are the second letters of the Latin alphabet and the ʾabjadī sequence respectively | ||
c | From the initial form of Arabic: ح ḥāʾ, or that of a dotless Arabic: ج jīm; c and Arabic: ج jīm are the third letters of the Latin alphabet and the ʾabjadī sequence respectively, and the letters also share a common ancestor and the same sound | ||
d | From the Arabic letter Arabic: د dāl; d and Arabic: د dāl are the fourth letters of the Latin alphabet and the ʾabjadī sequence respectively, and the letters also share a common ancestor and the same sound | ||
x | From the Arabic letter Arabic: س sīn. It is contested that the usage of Latin x in maths is derived from the first letter Arabic: ش šīn (without its dots) of the Arabic word Arabic: شيء šayʾ(un) pronounced as /ar/, meaning thing.[1] (X was used in old Spanish for the sound /ʃ/). However, according to others there is no historical evidence for this.[2] [3] | ||
y | From the Arabic letter Arabic: ص ṣād | ||
z | From the Arabic letter Arabic: ع ʿayn | ||
| Description | Latin | Arabic | Notes | |
|---|---|---|---|---|
| Euler's number | e | Initial form of the Arabic letter Arabic: ه hāʾ. Both Latin letter e and Arabic letter Arabic: ه hāʾ are descendants of Phoenician letter hē. | ||
| imaginary unit | i | From Arabic: ت tāʾ, which is in turn derived from the first letter of the second word of Arabic: وحدة تخيلية waḥdaẗun taḫīliyya "imaginary unit" | ||
| pi | \pi | From Arabic: ط ṭāʾ; also \pi | ||
| radius | r | From Arabic: ن nūn followed by a dotless Arabic: ق qāf, which is in turn derived from Arabic: نصف القطر nuṣfu l-quṭr "radius" | ||
| kilogram | kg | From Arabic: كجم kāf-jīm-mīm. In some regions alternative symbols like (kāf-ġayn) or (kāf-lām-ġayn) are used. All three abbreviations are derived from Arabic: كيلوغرام kīlūġrām "kilogram" and its variant spellings. | ||
| gram | g | From Arabic: جم jīm-mīm, which is in turn derived from Arabic: جرام jrām, a variant spelling of Arabic: غرام ġrām "gram" | ||
| metre | m | From Arabic: م mīm, which is in turn derived from Arabic: متر mitr "metre" | ||
| centimetre | cm | From Arabic: سم sīn-mīm, which is in turn derived from Arabic: سنتيمتر "centimetre" | ||
| millimetre | mm | From Arabic: مم mīm-mīm, which is in turn derived from Arabic: مليمتر millīmitr "millimetre" | ||
| kilometre | km | From Arabic: كم kāf-mīm; also (kāf-lām-mīm) in some regions; both are derived from Arabic: كيلومتر kīlūmitr "kilometre". | ||
| second | s | From Arabic: ث ṯāʾ, which is in turn derived from Arabic: ثانية ṯāniya "second" | ||
| minute | min | From Arabic: د dālʾ, which is in turn derived from Arabic: دقيقة daqīqa "minute"; also (i.e. dotless Arabic: ق qāf) in some regions | ||
| hour | h | From Arabic: س sīnʾ, which is in turn derived from Arabic: ساعة sāʿa "hour" | ||
| kilometre per hour | km/h | From the symbols for kilometre and hour | ||
| degree Celsius | °C | From Arabic: س sīn, which is in turn derived from the second word of Arabic: درجة سيلسيوس darajat sīlsīūs "degree Celsius"; also from Arabic: م mīmʾ, which is in turn derived from the first letter of the third word of Arabic: درجة حرارة مئوية "degree centigrade" | ||
| degree Fahrenheit | °F | From Arabic: ف fāʾ, which is in turn derived from the second word of Arabic: درجة فهرنهايت darajat fahranhāyt "degree Fahrenheit" | ||
| millimetres of mercury | mmHg | From Arabic: مم‌ز mīm-mīm zayn, which is in turn derived from the initial letters of the words Arabic: مليمتر زئبق "millimetres of mercury" | ||
| Ångström | Å | From Arabic: أْ ʾalif with hamzah and ring above, which is in turn derived from the first letter of "Ångström", variously spelled Arabic: أنغستروم or Arabic: أنجستروم | ||
| Description | Latin | Arabic | Notes | |
|---|---|---|---|---|
| Natural numbers | N | From Arabic: ط ṭāʾ, which is in turn derived from the first letter of the second word of Arabic: عدد طبيعي ʿadadun ṭabīʿiyyun "natural number" | ||
| Integers | Z | From Arabic: ص ṣād, which is in turn derived from the first letter of the second word of Arabic: عدد صحيح ʿadadun ṣaḥīḥun "integer" | ||
| Rational numbers | Q | From Arabic: ن nūn, which is in turn derived from the first letter of Arabic: نسبة nisba "ratio" | ||
| Real numbers | R | From Arabic: ح ḥāʾ, which is in turn derived from the first letter of the second word of Arabic: عدد حقيقي ʿadadun ḥaqīqiyyun "real number" | ||
| Imaginary numbers | I | From Arabic: ت tāʾ, which is in turn derived from the first letter of the second word of Arabic: عدد تخيلي ʿadadun taḫīliyyun "imaginary number" | ||
| Complex numbers | C | From Arabic: م mīm, which is in turn derived from the first letter of the second word of Arabic: عدد مركب ʿadadun murakkabun "complex number" | ||
| Empty set | \varnothing | \varnothing | ∅ | |
| Is an element of | \in | \ni | ∈ | A mirrored ∈ |
| Subset | \subset | \supset | ⊂ | A mirrored ⊂ |
| Superset | \supset | \subset | ⊃ | A mirrored ⊃ |
| Universal set | S | From Arabic: ش šīn, which is in turn derived from the first letter of the second word of Arabic: مجموعة شاملة majmūʿatun šāmila "universal set" | ||
| Description | Latin/Greek | Arabic | Notes | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Percent | % | e.g. 100% "Arabic: ٪١٠٠ " | ||||||||
| Permille | ‰ | is an Arabic equivalent of the per ten thousand sign ‱. | ||||||||
| Is proportional to | \propto | ∝ | A mirrored ∝ | |||||||
| n th root | \sqrt[n]{} | Arabic: ں is a dotless Arabic: ن nūn while √ is a mirrored radical sign √ | ||||||||
| Logarithm | log | From Arabic: لو lām-wāw, which is in turn derived from لوغاريتم "logarithm" | ||||||||
| Logarithm to base b | logb | |||||||||
| Natural logarithm | ln | From the symbols of logarithm and Euler's number | ||||||||
| Summation | \sum | Arabic: مجـــ mīm-medial form of jīm is derived from the first two letters of Arabic: مجموع majmūʿ "sum"; also (∑, a mirrored summation sign ∑) in some regions | ||||||||
| Product | \prod | From Arabic: جذ jīm-ḏāl. The Arabic word for "product" is جداء jadāʾun. Also \prod | ||||||||
| Factorial | n! | Also in some regions | ||||||||
| Permutations |
| Also is used in some regions as P(n,r) | ||||||||
| Combinations |
| Also is used in some regions as C(n,k) n\choosek | ||||||||
| Description | Latin | Arabic | Notes | ||
|---|---|---|---|---|---|
| Sine | \sin | from Arabic: حاء ḥāʾ (i.e. dotless Arabic: ج jīm)-ʾalif; also (jīm-bāʾ) is used in some regions (e.g. Syria); Arabic for "sine" is Arabic: جيب jayb | |||
| Cosine | \cos | from Arabic: حتا ḥāʾ (i.e. dotless Arabic: ج jīm)-tāʾ-ʾalif; also (tāʾ-jīm-bāʾ) is used in some regions (e.g. Syria); Arabic for "cosine" is Arabic: جيب تمام | |||
| Tangent | \tan | from Arabic: طا ṭāʾ (i.e. dotless Arabic: ظ ẓāʾ)-ʾalif; also (ẓāʾ-lām) is used in some regions (e.g. Syria); Arabic for "tangent" is Arabic: ظل ẓill | |||
| Cotangent | \cot | from Arabic: طتا ṭāʾ (i.e. dotless Arabic: ظ ẓāʾ)-tāʾ-ʾalif; also (tāʾ-ẓāʾ-lām) is used in some regions (e.g. Syria); Arabic for "cotangent" is Arabic: ظل تمام | |||
| Secant | \sec | from Arabic: ٯا dotless Arabic: ق qāf-ʾalif; Arabic for "secant" is Arabic: قاطع | |||
| Cosecant | \csc | from Arabic: ٯتا dotless Arabic: ق qāf-tāʾ-ʾalif; Arabic for "cosecant" is Arabic: قاطع تمام | |||
The letter (zayn, from the first letter of the second word of Arabic: دالة زائدية "hyperbolic function") is added to the end of trigonometric functions to express hyperbolic functions. This is similar to the way
\operatorname{h}
| Description | Hyperbolic sine | Hyperbolic cosine | Hyperbolic tangent | Hyperbolic cotangent | Hyperbolic secant | Hyperbolic cosecant | |
|---|---|---|---|---|---|---|---|
| Latin | \sinh | \cosh | \tanh | \coth | \operatorname{sech} | \operatorname{csch} | |
| Arabic | |||||||
For inverse trigonometric functions, the superscript in Arabic notation is similar in usage to the superscript
-1
| Description | Inverse sine | Inverse cosine | Inverse tangent | Inverse cotangent | Inverse secant | Inverse cosecant | |
|---|---|---|---|---|---|---|---|
| Latin | \sin-1 | \cos-1 | \tan-1 | \cot-1 | \sec-1 | \csc-1 | |
| Arabic | |||||||
| Description | Inverse hyperbolic sine | Inverse hyperbolic cosine | Inverse hyperbolic tangent | Inverse hyperbolic cotangent | Inverse hyperbolic secant | Inverse hyperbolic cosecant | |
|---|---|---|---|---|---|---|---|
| Latin | \sinh-1 | \cosh-1 | \tanh-1 | \coth-1 | \operatorname{sech}-1 | \operatorname{csch}-1 | |
| Arabic | |||||||
| Description | Latin | Arabic | Notes | |
|---|---|---|---|---|
| Limit | \lim | Arabic: نهــــا nūn-hāʾ-ʾalif is derived from the first three letters of Arabic Arabic: نهاية nihāya "limit" | ||
| Function | f(x) | Arabic: د dāl is derived from the first letter of Arabic: دالة "function". Also called Arabic: تابع, Arabic: تا for short, in some regions. | ||
| Derivatives | f'(x),\dfrac{dy}{dx},\dfrac{d2y}{dx2},\dfrac{\partial{y}}{\partial{x}} | ‵ is a mirrored prime ′ while ، is an Arabic comma. The signs should be mirrored: ∂. | ||
| Integrals | \int{},\iint{},\iiint{},\oint{} | ‪∮ ،∭ ،∬ ،∫‬ | Mirrored ∫, ∬, ∭ and ∮ | |