Modern Arabic Mathematical Notation
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Modern Arabic Mathematical Notation

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.

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 (Arabic pronunciation: [n?q]), which is written using the two letters n?n and q?f. 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.

Table of numerals
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.

Mirrored Latin symbols

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

Arabic mathematical limit in different forms
Latin Arabic Persian
x4 [a] [b]
  • ^a ?n?n-h-?alif is derived from the first three letters of Arabic nih?ya "limit".
  • ^b ?add is Persian for "limit".

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

Arabic mathematical sum in different forms
Latin Arabic Mirrored Latin
?‭?‬?[c] 3‭?‬?

ma?m means "sum" in Arabic.

However, in Iran, usually Latin symbols are used.

Examples

Mathematical letters

Latin Arabic Notes
Arabic mathematical alif.PNG ? From the Arabic letter ??alif; a and ??alif are the first letters of the Latin alphabet and the Arabic alphabet's ?abjad? sequence respectively
Arabic mathematical beh.PNG ? A dotless ?b; b and ?b are the second letters of the Latin alphabet and the ?abjad? sequence respectively
Arabic mathematical geem.PNG 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
Arabic mathematical dal.PNG ? From the Arabic letter ?d?l; d and ?d?l are the fourth letters of the Latin alphabet and the ?abjad? sequence respectively
Arabic mathematical seen.PNG ? 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]
Arabic mathematical sad.PNG ? From the Arabic letter ?d
Arabic mathematical ain.PNG ? From the Arabic letter ??ayn

Mathematical constants and units

Description Latin Arabic Notes
Euler's number Arabic mathematical heh.PNG ? Initial form of the Arabic letter ?h. Both Latin letter e and Arabic letter ?h are descendants of Phoenician letter Phoenician he.svg h?.
imaginary unit Arabic mathematical teh.PNG ? From ?t, which is in turn derived from the first letter of the second word of ? wa?da?un taliyya "imaginary unit"
pi Arabic mathematical tah.PNG ? From ?; also in some regions
radius Arabic mathematical radius.PNG From ?n?n followed by a dotless ?q?f, which is in turn derived from nu?fu l-qu?r "radius"
kilogram kg Arabic kilogram.PNG From k?f-j?m-m?m. In some regions alternative symbols like Arabic alternative kilogram 2.PNG ( k?f-?ayn) or Arabic alternative kilogram 1.PNG ( k?f-l?m-?ayn) are used. All three abbreviations are derived from k?lr?m "kilogram" and its variant spellings.
gram g Arabic gram.PNG From j?m-m?m, which is in turn derived from ?jr?m, a variant spelling of ??r?m "gram"
meter m Arabic mathematical meem.PNG ? From ?m?m, which is in turn derived from mitr "meter"
centimeter cm Arabic cm.PNG From s?n-m?m, which is in turn derived from ?‎ "centimeter"
millimeter mm Arabic mm.PNG From m?m-m?m, which is in turn derived from mill?mitr "millimeter"
kilometer km Arabic Km.PNG From k?f-m?m; also Arabic alternative km.PNG ( k?f-l?m-m?m) in some regions; both are derived from ?k?l?mitr "kilometer".
second s Arabic mathematical theh.PNG ? From ?, which is in turn derived from niya "second"
minute min Arabic mathematical Dal large.PNG ? From ?d?l?, which is in turn derived from daq?qa "minute"; also Arabic mathematical qaf.PNG ( ?, i.e. dotless ?q?f) in some regions
hour h Arabic mathematical seen.PNG ? From ?s?n?, which is in turn derived from ?sa "hour"
kilometer per hour km/h Arabic kmph.PNG /? From the symbols for kilometer and hour
degree Celsius °C Arabic celsius degree.PNG °? From ?s?n, which is in turn derived from the second word of ? ?darajat s?lss "degree Celsius"; also Arabic centegrade degree.PNG ( °?) from ?m?m?, which is in turn derived from the first letter of the third word of ? ‎ "degree centigrade"
degree Fahrenheit °F Arabic fahrenheit degree.PNG °? From ?f, which is in turn derived from the second word of ? darajat fahranh?yt "degree Fahrenheit"
millimeters of mercury mmHg Arabic mmHg.PNG ‌? From ‌?m?m-m?m zayn, which is in turn derived from the initial letters of the words ?‎ "millimeters of mercury"
Ångström Å Arabic angestrom.PNG From ?alif with hamzah and ring above, which is in turn derived from the first letter of "Ångström", variously spelled ‎ or

Sets and number systems

Description Latin Arabic Notes
Natural numbers Arabic mathematical tah large.PNG ? From ?, which is in turn derived from the first letter of the second word of ?adadun ?abiyyun "natural number"
Integers Arabic mathematical Sad large.PNG ? From ?d, which is in turn derived from the first letter of the second word of ??adadun ?aun "integer"
Rational numbers Arabic mathematical noon large.PNG ? From ?n?n, which is in turn derived from the first letter of ?nisba "ratio"
Real numbers Arabic mathematical hah large.PNG ? From ?, which is in turn derived from the first letter of the second word of ?adadun ?aq?qiyyun "real number"
Imaginary numbers Arabic mathematical teh large.PNG ? From ?t, which is in turn derived from the first letter of the second word of ?adadun taliyyun "imaginary number"
Complex numbers Arabic mathematical meem large.PNG ? 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 Arabic mathematical sheen large.PNG ? From ?n, which is in turn derived from the first letter of the second word of majmatun mila "universal set"

Arithmetic and algebra

Description Latin Arabic Notes
Percent % Arabic percent.PNG ? e.g. 100% "?‎"
Permille ? Arabic permille.PNG ? ? is an Arabic equivalent of the per ten thousand sign ?.
Is proportional to Arabic prop.PNG ? A mirrored ?
n th root Arabic mathematical nth root.PNG ?‭?‬ ?‎ is a dotless ?n?n while ? is a mirrored radical sign ?
Logarithm Arabic mathematical log.PNG From l?m-w?w, which is in turn derived from lr?tm "logarithm"
Logarithm to base b Arabic mathematical log b.PNG ?
Natural logarithm Arabic mathematical ln.PNG ? From the symbols of logarithm and Euler's number
Summation Arabic mathematical sum.PNG m?m-medial form of j?m is derived from the first two letters of majm "sum"; also Arabic mathematical mirrored sum.PNG (?, a mirrored summation sign ?) in some regions
Product Arabic mathematical product.PNG From j?m-l. The Arabic word for "product" is ? jadun. Also in some regions.
Factorial Arabic mathematical factorial.PNG ? Also Arabic mathematical fact.PNG ( ?!) in some regions
Permutations Arabic mathematical nPr.PNG ??? Also Arabic mathematical P(n,r).PNG ( ?( ?)) is used in some regions as
Combinations Arabic mathematical nCk.PNG ??? Also Arabic mathematical C(n,k).PNG ( ?( ?)) is used in some regions as and Arabic mathematical b(n,k).PNG (?
?
) as the binomial coefficient

Trigonometric and hyperbolic functions

Trigonometric functions

Description Latin Arabic Notes
Sine Arabic mathematical sin.PNG from (i.e. dotless ?j?m)-?alif; also Arabic mathematical sins.PNG ( j?m-b) is used in some regions (e.g. Syria); Arabic for "sine" is jayb
Cosine Arabic mathematical cos.PNG from (i.e. dotless ?j?m)-t-?alif; also Arabic mathematical coss.PNG ( t-j?m-b) is used in some regions (e.g. Syria); Arabic for "cosine" is ?
Tangent Arabic mathematical tan.PNG from (i.e. dotless ?)-?alif; also Arabic mathematical tans.PNG ( -l?m) is used in some regions (e.g. Syria); Arabic for "tangent" is ?ill
Cotangent Arabic mathematical cot.PNG from (i.e. dotless ?)-t-?alif; also Arabic mathematical cots.PNG ( t--l?m) is used in some regions (e.g. Syria); Arabic for "cotangent" is ?
Secant Arabic mathematical sec.PNG from ‎ dotless ?q?f-?alif; Arabic for "secant" is ?
Cosecant Arabic mathematical csc.PNG from ‎ dotless ?q?f-t-?alif; Arabic for "cosecant" is ? ?

Hyperbolic functions

The letter Arabic mathematical zain.PNG ( ? 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.

Arabic hyperbolic functions
Description Hyperbolic sine Hyperbolic cosine Hyperbolic tangent Hyperbolic cotangent Hyperbolic secant Hyperbolic cosecant
Latin
Arabic ? ? ?

Inverse trigonometric functions

For inverse trigonometric functions, the superscript -? in Arabic notation is similar in usage to the superscript in Latin-based notation.

Arabic inverse trigonometric functions
Description Inverse sine Inverse cosine Inverse tangent Inverse cotangent Inverse secant Inverse cosecant
Latin
Arabic -? -? -? -? -? -?

Inverse hyperbolic functions

Arabic inverse hyperbolic functions
Description Inverse hyperbolic sine Inverse hyperbolic cosine Inverse hyperbolic tangent Inverse hyperbolic cotangent Inverse hyperbolic secant Inverse hyperbolic cosecant
Latin
Arabic -? ?-? -? ?-? -? ?-?

Calculus

Description Latin Arabic Notes
Limit Arabic mathematical limit.PNG ? ?n?n-h-?alif is derived from the first three letters of Arabic nih?ya "limit"
function Arabic mathematical f(x).PNG ?(?) ?d?l is derived from the first letter of ?‎ "function". Also called ?‎, ‎ for short, in some regions.
derivatives Arabic mathematical derivatives.PNG ?`(?)? ?‌?/ ?‌? ? ???/ ?‌?? ? ??/?? ` is a mirrored prime ? while ? is an Arabic comma. The ? signs should be mirrored: ?.
Integrals Arabic mathematical integrals.PNG ? ?? ?? ?? Mirrored ?, ?, ? and ?

Complex analysis

Latin Arabic
Arabic mathematical complex analysis.PNG
? = ? + ? ? = ?( ? + ? ?) = ? ??‌? = ???

See also

References

  1. ^ Moore, Terry. "Why is X the Unknown". Ted Talk.
  2. ^ Cajori, Florian (1993). A History of Mathematical Notation. Courier Dover Publications. pp. 382-383. Retrieved 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.

External links


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