Modern Arabic mathematical notation

From Wikipedia, the free encyclopedia
Jump to: navigation, search

The designation modern Arabic mathematical notation is used for a mathematical notation based on the Arabic script, 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.


  • 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.


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[edit]

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

Table of numerals

Mirrored Latin symbols[edit]

Sometimes, symbols used in Arabic mathematical notation differ according to the region:

Arabic mathematical limit in different forms

Sometimes, mirrored Latin symbols are used in Arabic mathematical notation (especially in western Arabic regions):

Arabic mathematical sum in different forms

However, in Iran, usually Latin symbols are used.


Mathematical letters[edit]

Latin Arabic
a Arabic mathematical alif.PNG
b Arabic mathematical beh.PNG
c Arabic mathematical geem.PNG
d Arabic mathematical dal.PNG
x Arabic mathematical seen.PNG
y Arabic mathematical sad.PNG
z Arabic mathematical ain.PNG
  • It is contested that the usage of Latin x in maths is derived from the first letter of the Arabic word شيء [ʃajʔ(un)] 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]

Mathematical constants and units[edit]

Description Latin Arabic Notes
Euler's number e Arabic mathematical heh.PNG
imaginary unit i Arabic mathematical teh.PNG
pi \pi Arabic mathematical tah.PNG also \pi in some regions
radius r Arabic mathematical radius.PNG
kilogram kg Arabic kilogram.PNG In some regions alternative symbols like Arabic alternative kilogram 2.PNG or Arabic alternative kilogram 1.PNG are used
gram g Arabic gram.PNG
meter m Arabic mathematical meem.PNG
centimeter cm Arabic cm.PNG
millimeter mm Arabic mm.PNG
kilometer km Arabic Km.PNG also Arabic alternative km.PNG in some regions
second s Arabic mathematical theh.PNG
minute min Arabic mathematical Dal large.PNG also Arabic mathematical qaf.PNG in some regions
hour h Arabic mathematical seen.PNG
kilometer per hour km/h Arabic kmph.PNG
degree Celsius °C Arabic celsius degree.PNG also Arabic centegrade degree.PNG
degree Fahrenheit °F Arabic fahrenheit degree.PNG
millimeters of mercury mmHg Arabic mmHg.PNG
Ångström Å Arabic angestrom.PNG

Sets and number systems[edit]

Description Latin Arabic
Natural numbers \mathbb{N} Arabic mathematical tah large.PNG
Integers \mathbb{Z} Arabic mathematical Sad large.PNG
Rational numbers \mathbb{Q} Arabic mathematical noon large.PNG
Real numbers \mathbb{R} Arabic mathematical hah large.PNG
Imaginary numbers \mathbb{I} Arabic mathematical teh large.PNG
Complex numbers \mathbb{C} Arabic mathematical meem large.PNG
Empty set \varnothing \varnothing
Is an element of \in \ni
Subset \subset \supset
Superset \supset \subset
Universal set \mathbf{S} Arabic mathematical sheen large.PNG

Arithmetic and algebra[edit]

Description Latin Arabic Notes
Percent  % Arabic percent.PNG
Permille Arabic permille.PNG
Is proportional to \propto Arabic prop.PNG
n th root  \sqrt[n]{\,\,\,} Arabic mathematical nth root.PNG
Logarithm \log Arabic mathematical log.PNG
Logarithm to base b \log_b Arabic mathematical log b.PNG
Natural logarithm \ln Arabic mathematical ln.PNG
Summation \sum Arabic mathematical sum.PNG also Arabic mathematical mirrored sum.PNG in some regions
Product \prod Arabic mathematical product.PNG also \prod in some regions
factorial n! Arabic mathematical factorial.PNG also Arabic mathematical fact.PNG in some regions
permutations ^n\mathbf{P}_r Arabic mathematical nPr.PNG also Arabic mathematical P(n,r).PNG is used in some regions as \mathbf{P}(n,r)
Combinations ^n\mathbf{C}_k Arabic mathematical nCk.PNG also Arabic mathematical C(n,k).PNGis used in some regions as \mathbf{C}(n,k)
and Arabic mathematical b(n,k).PNG as the binomial coefficient  n \choose k

Trigonometric and hyperbolic functions[edit]

Trigonometric functions[edit]

Latin Arabic Notes
\sin Arabic mathematical sin.PNG also Arabic mathematical sins.PNG is used in some regions (e.g. : Syria)
\cos Arabic mathematical cos.PNG also Arabic mathematical coss.PNG is used in some regions (e.g. : Syria)
\tan Arabic mathematical tan.PNG also Arabic mathematical tans.PNG is used in some regions (e.g. : Syria)
\cot Arabic mathematical cot.PNG also Arabic mathematical cots.PNG is used in some regions (e.g. : Syria)
\sec Arabic mathematical sec.PNG
\csc Arabic mathematical csc.PNG

Hyperbolic functions[edit]

The letter Arabic mathematical zain.PNGis added to the end of trigonometric functions to express hyperbolic functions (the same way h is used in Latin notation).
Arabic hyperbolic functions

Inverse trigonometric functions[edit]

The notation sin^{-1} is the one used in Arabic notation for the inverse functions like:
Arabic inverse trigonometric functions

Inverse hyperbolic functions[edit]

Arabic inverse hyperbolic functions


Description Latin Arabic Notes
Limit \lim Arabic mathematical limit.PNG
function \mathbf{f}(x) Arabic mathematical f(x).PNG
derivatives \mathbf{f'}(x), \dfrac{dy}{dx} , \dfrac{d^2y}{dx^2} , \dfrac{\partial {y}}{\partial{x}} Arabic mathematical derivatives.PNG
Integrals \int{} , \iint{} ,\iiint{}, \oint{} Arabic mathematical integrals.PNG

Complex analysis[edit]

Latin Arabic
z = x + iy = r(\cos{\varphi}+i \sin{\varphi})= r e^{i\varphi} = r\angle{\varphi} Arabic mathematical complex analysis.PNG

See also[edit]

External links[edit]


  1. ^ Moore, Terry. "Why is X the Unknown". Ted Talk. 
  2. ^ 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.' 
  3. ^ 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.