1 Features 2 Variations
2.1 Numeral systems 2.2 Mirrored Latin symbols
3.1 Mathematical letters 3.2 Mathematical constants and units 3.3 Sets and number systems 3.4 Arithmetic and algebra 3.5 Trigonometric and hyperbolic functions
3.5.1 Trigonometric functions 3.5.2 Hyperbolic functions 3.5.3 Inverse trigonometric functions 3.5.4 Inverse hyperbolic functions
3.6 Calculus 3.7 Complex analysis
4 See also 5 References 6 External links
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) 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 نق (Arabic pronunciation: [nɑq]), which is written using the two letters nūn and qāf. 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, 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 and Urdu speaking regions (e.g. Iran, Pakistan, India)
European(descended from Western Arabic)
0 1 2 3 4
5 6 7 8 9
Arabic-Indic (Eastern Arabic)
٠ ١ ٢ ٣ ٤
٥ ٦ ٧ ٨ ٩
۰ ۱ ۲ ۳ ۴
۵ ۶ ۷ ۸ ۹
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. ٣٫١٤١٥٩٢٦٥٣٥٨ 3.14159265358, ١٬٠٠٠٬٠٠٠٬٠٠٠ 1,000,000,000. Negative signs are written to the left of magnitudes, e.g. ٣− −3. In-line fractions are written with the numerator and denominator on the left and right of the fraction slash respectively, e.g. ٢/٧ 2/7.
Mirrored Latin symbols Sometimes, symbols used in Arabic mathematical notation differ according to the region:
lim x→∞ x4
نهــــــــــــا س←∞ س٤ [a]
حــــــــــــد س←∞ س۴ [b]
^a نهــــا nūn-hāʾ-ʾalif is derived from the first three letters of Arabic نهاية nihāya "limit". ^b حد ḥadd is Persian for "limit".
Sometimes, mirrored Latin symbols are used in Arabic mathematical notation (especially in western Arabic regions):
n ∑ x=0 3√x
ں مجــــــــــــ س=٠ ٣√س[c]
^c مجــــ mīm-medial form of ǧīm is derived from the first two letters of Arabic مجموع maǧmūʿ "sum".
However, in Iran, usually Latin symbols are used.
Examples Mathematical letters
ا From the Arabic letter ا ʾalif; a and ا ʾalif are the first letters of the Latin alphabet and the Arabic alphabet's ʾabjadī sequence respectively
ٮ A dotless ب bāʾ; b and ب bāʾ are the second letters of the Latin alphabet and the ʾabjadī sequence respectively
حــــ From the initial form of ح ḥāʾ, or that of a dotless ج jīm; c and ج jīm are the third letters of the Latin alphabet and the ʾabjadī sequence respectively
د From the Arabic letter د dāl; d and د dāl are the fourth letters of the Latin alphabet and the ʾabjadī sequence respectively
س From the Arabic letter س sīn. It is contested that the usage of Latin x in maths is derived from the first letter ش šīn (without its dots) of the Arabic word شيء šayʾ(un) [ʃajʔ(un)], meaning thing. (X was used in old Spanish for the sound /ʃ/). However, according to others there is no historical evidence for this.
ص From the Arabic letter ص ṣād
ع From the Arabic letter ع ʿayn
Mathematical constants and units
Initial form of the Arabic letter ه hāʾ. Both Latin letter e and Arabic letter ه hāʾ are descendants of Phoenician letter hē.
From ت tāʾ, which is in turn derived from the first letter of the second word of وحدة تخيلية waḥdaẗun taḫīliyya "imaginary unit"
From ط ṭāʾ; also
in some regions
From ن nūn followed by a dotless ق qāf, which is in turn derived from نصف القطر nuṣfu l-quṭr "radius"
From كجم kāf-jīm-mīm. In some regions alternative symbols like ( كغ kāf-ġayn) or ( كلغ kāf-lām-ġayn) are used. All three abbreviations are derived from كيلوغرام kīlūġrām "kilogram" and its variant spellings.
From جم jīm-mīm, which is in turn derived from جرام jrām, a variant spelling of غرام ġrām "gram"
From م mīm, which is in turn derived from متر mitr "meter"
From سم sīn-mīm, which is in turn derived from سنتيمتر "centimeter"
From مم mīm-mīm, which is in turn derived from مليمتر millīmitr "millimeter"
From كم kāf-mīm; also ( كلم kāf-lām-mīm) in some regions; both are derived from كيلومتر kīlūmitr "kilometer".
From ث ṯāʾ, which is in turn derived from ثانية ṯāniya "second"
From د dālʾ, which is in turn derived from دقيقة daqīqa "minute"; also ( ٯ , i.e. dotless ق qāf) in some regions
From س sīnʾ, which is in turn derived from ساعة sāʿa "hour"
kilometer per hour
From the symbols for kilometer and hour
From س sīn, which is in turn derived from the second word of درجة سيلسيوس darajat sīlsīūs "degree Celsius"; also ( °م ) from م mīmʾ, which is in turn derived from the first letter of the third word of درجة حرارة مئوية "degree centigrade"
From ف fāʾ, which is in turn derived from the second word of درجة فهرنهايت darajat fahranhāyt "degree Fahrenheit"
millimeters of mercury
From ممز mīm-mīm zayn, which is in turn derived from the initial letters of the words مليمتر زئبق "millimeters of mercury"
From أْ ʾalif with hamzah and ring above, which is in turn derived from the first letter of "Ångström", variously spelled أنغستروم or أنجستروم
Sets and number systems
displaystyle mathbb N
From ط ṭāʾ, which is in turn derived from the first letter of the second word of عدد طبيعيʿadadun ṭabīʿiyyun "natural number"
displaystyle mathbb Z
From ص ṣād, which is in turn derived from the first letter of the second word of عدد صحيح ʿadadun ṣaḥīḥun "integer"
displaystyle mathbb Q
From ن nūn, which is in turn derived from the first letter of نسبة nisba "ratio"
displaystyle mathbb R
From ح ḥāʾ, which is in turn derived from the first letter of the second word of عدد حقيقي ʿadadun ḥaqīqiyyun "real number"
displaystyle mathbb I
From ت tāʾ, which is in turn derived from the first letter of the second word of عدد تخيلي ʿadadun taḫīliyyun "imaginary number"
displaystyle mathbb C
From م mīm, which is in turn derived from the first letter of the second word of عدد مركب ʿadadun markabun "complex number"
Is an element of
A mirrored ∈
A mirrored ⊂
A mirrored ⊃
displaystyle mathbf S
From ش šīn, which is in turn derived from the first letter of the second word of مجموعة شاملة majmūʿatun šāmila "universal set"
Arithmetic and algebra
e.g. 100% "٪١٠٠"
؊ is an Arabic equivalent of the per ten thousand sign ‱.
Is proportional to
A mirrored ∝
n th root
displaystyle sqrt[ n ] ,,,
ں is a dotless ن nūn while √ is a mirrored radical sign √
From لو lām-wāw, which is in turn derived from لوغاريتم lūġārītm "logarithm"
Logarithm to base b
displaystyle log _ b
From the symbols of logarithm and Euler's number
مجـــ mīm-medial form of jīm is derived from the first two letters of مجموع majmūʿ "sum"; also (∑, a mirrored summation sign ∑) in some regions
From جذ jīm-ḏāl. The Arabic word for "product" is جداء jadāʾun. Also
in some regions.
Also ( ں! ) in some regions
displaystyle ^ n mathbf P _ r
Also ( ل(ں، ر) ) is used in some regions as
( n , r )
displaystyle mathbf P (n,r)
displaystyle ^ n mathbf C _ k
Also ( ٯ(ں، ك) ) is used in some regions as
( n , k )
displaystyle mathbf C (n,k)
and ( ⎛⎝ںك⎞⎠ ) as the binomial coefficient
displaystyle n choose k
Trigonometric and hyperbolic functions Trigonometric functions
from حاء ḥāʾ (i.e. dotless ج jīm)-ʾalif; also ( جب jīm-bāʾ) is used in some regions (e.g. Syria); Arabic for "sine" is جيب jayb
from حتا ḥāʾ (i.e. dotless ج jīm)-tāʾ-ʾalif; also ( تجب tāʾ-jīm-bāʾ) is used in some regions (e.g. Syria); Arabic for "cosine" is جيب تمام
from طا ṭāʾ (i.e. dotless ظ ẓāʾ)-ʾalif; also ( ظل ẓāʾ-lām) is used in some regions (e.g. Syria); Arabic for "tangent" is ظل ẓill
from طتا ṭāʾ (i.e. dotless ظ ẓāʾ)-tāʾ-ʾalif; also ( تظل tāʾ-ẓāʾ-lām) is used in some regions (e.g. Syria); Arabic for "cotangent" is ظل تمام
from ٯا dotless ق qāf-ʾalif; Arabic for "secant" is أو قاطع
from ٯتا dotless ق qāf-tāʾ-ʾalif; Arabic for "cosecant" is أو قاطع تمام
Hyperbolic functions The letter ( ز zayn, from the first letter of the second word of دالة زائدية "hyperbolic function") is added to the end of trigonometric functions to express hyperbolic functions. This is similar to the way
displaystyle operatorname h
is added to the end of trigonometric functions in Latin-based notation.
displaystyle operatorname sech
displaystyle operatorname csch
Inverse trigonometric functions For inverse trigonometric functions, the superscript −١ in Arabic notation is similar in usage to the superscript
in Latin-based notation.
displaystyle sin ^ -1
displaystyle cos ^ -1
displaystyle tan ^ -1
displaystyle cot ^ -1
displaystyle sec ^ -1
displaystyle csc ^ -1
Inverse hyperbolic functions
Inverse hyperbolic sine
Inverse hyperbolic cosine
Inverse hyperbolic tangent
Inverse hyperbolic cotangent
Inverse hyperbolic secant
Inverse hyperbolic cosecant
displaystyle sinh ^ -1
displaystyle cosh ^ -1
displaystyle tanh ^ -1
displaystyle coth ^ -1
displaystyle operatorname sech ^ -1
displaystyle operatorname csch ^ -1
نهــــا nūn-hāʾ-ʾalif is derived from the first three letters of Arabic نهاية nihāya "limit"
( x )
displaystyle mathbf f (x)
د dāl is derived from the first letter of دالة "function". Also called تابع, تا for short, in some regions.
( x ) ,
displaystyle mathbf f' (x), dfrac dy dx , dfrac d^ 2 y dx^ 2 , dfrac partial y partial x
د‵(س)، دص/ دس ، د٢ص/ دس٢ ، ∂ص/ ∂س
‵ is a mirrored prime ′ while ، is an Arabic comma. The ∂ signs should be mirrored: ∂.
displaystyle int ,iint ,iiint ,oint
∫ ،∬ ،∭ ،∮
Mirrored ∫, ∬, ∭ and ∮
z = x + i y = r ( cos
+ i sin
) = r
= r ∠
displaystyle z=x+iy=r(cos varphi +isin varphi )=re^ ivarphi =rangle varphi
ع = س + ت ص = ل(حتا ى + ت حا ى) = ل ھتى = ل∠ى
See also Mathematical notation Arabic Mathematical Alphabetic Symbols References
^ Moore, Terry. "Why is X the Unknown". Ted Talk.
^ Cajori, Florian. A History of Mathematical Notation. Courier Dover Publications. pp. 382–383. Retrieved 11 October 2012. 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.'
^ Oxford Dictionary, 2nd Edition. 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.
External links Multilingual mathematical e-document processing Arabic mathematical notation - W3C Interest Group Note. Arabic math editor