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.
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.
Variationsedit
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 symbols used.
Numeral systemsedit
There are three numeral systems used in right to left mathematical notation.
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. ٣٫١٤١٥٩٢٦٥٣٥٨3.14159265358, ١٬٠٠٠٬٠٠٠٬٠٠٠1,000,000,000. 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. ٢/٧2/7.
Symbolsedit
Sometimes, symbols used in Arabic mathematical notation differ according to the region:
From the Arabic letterاʾalif; a and اʾalif 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
ٮ
A dotlessبbāʾ; b and بbāʾ are the second letters of the Latin alphabet and the ʾabjadī sequence respectively
حــــ
From the initial form of حḥāʾ, or that of a dotless جjīm; c and جjīm 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
د
From the Arabic letter دdāl; d and دdāl 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
س
From the Arabic letter سsīn. It is contested that the usage of Latin x in maths is derived from the first letter شšīn (without its dots) of the Arabic word شيءšayʾ(un)[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]
From كجمkāf-jīm-mīm. In some regions alternative symbols like (كغkāf-ġayn) or (كلغkāf-lām-ġayn) are used. All three abbreviations are derived from كيلوغرامkīlūġrām "kilogram" and its variant spellings.
From سsīn, which is in turn derived from the second word of درجة سيلسيوسdarajat sīlsīūs "degree Celsius"; also (°م) from مmīmʾ, which is in turn derived from the first letter of the third word of درجة حرارة مئوية "degree centigrade"
The letter (زzayn, 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 is added to the end of trigonometric functions in Latin-based notation.
^Moore, Terry. . Ted Talk. Archived from the original on 2014-02-22. Retrieved 2012-10-11.
^Cajori, Florian (1993). A History of Mathematical Notation. Courier Dover Publications. pp. 382–383. ISBN9780486677668. 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 linksedit
Multilingual mathematical e-document processing
Arabic mathematical notation - W3C Interest Group Note.
modern, arabic, mathematical, notation, mathematical, notation, based, arabic, script, used, especially, university, levels, education, form, mostly, derived, from, western, notation, some, notable, features, that, apart, from, western, counterpart, most, rema. 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 Contents 1 Features 2 Variations 2 1 Numeral systems 2 2 Symbols 3 Examples 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 linksFeatures editIt 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 nun and qaf When variable names are juxtaposed as when expressing multiplication they are written non cursively Variations editNotation 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 symbols used Numeral systems edit 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 Perso Arabic variant ۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹ Urdu variant nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp nbsp 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 Symbols edit Sometimes symbols used in Arabic mathematical notation differ according to the region nbsp Latin Arabic Persian lim x x4 س٤ نهــــــــــــا س a س۴ حــــــــــــد س b a نهــــا nun haʾ ʾalif is derived from the first three letters of Arabic نهاية nihaya limit b حد ḥadd is Persian for limit Sometimes mirrored Latin and Greek symbols are used in Arabic mathematical notation especially in western Arabic regions nbsp Latin Arabic Mirrored Latin and Greek n x 0 3 x ٣ س ں مجــــــــــــ س ٠ c 3 س ں س 0 c مجــــ is derived from Arabic مجموع maǧmuʿ sum However in Iran usually Latin and Greek symbols are used Examples editMathematical letters edit Latin Arabic Notes a displaystyle a nbsp nbsp ا From the Arabic letter ا ʾalif a and ا ʾalif are the first letters of the Latin alphabet and the Arabic alphabet s ʾabjadi sequence respectively and the letters also share a common ancestor and the same sound b displaystyle b nbsp nbsp ٮ A dotless ب baʾ b and ب baʾ are the second letters of the Latin alphabet and the ʾabjadi sequence respectively c displaystyle c nbsp nbsp حــــ From the initial form of ح ḥaʾ or that of a dotless ج jim c and ج jim are the third letters of the Latin alphabet and the ʾabjadi sequence respectively and the letters also share a common ancestor and the same sound d displaystyle d nbsp nbsp د From the Arabic letter د dal d and د dal are the fourth letters of the Latin alphabet and the ʾabjadi sequence respectively and the letters also share a common ancestor and the same sound x displaystyle x nbsp nbsp س From the Arabic letter س sin It is contested that the usage of Latin x in maths is derived from the first letter ش sin without its dots of the Arabic word شيء sayʾ un 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 y displaystyle y nbsp nbsp ص From the Arabic letter ص ṣad z displaystyle z nbsp nbsp ع From the Arabic letter ع ʿayn Mathematical constants and units edit Description Latin Arabic Notes Euler s number e displaystyle e nbsp nbsp ھ Initial form of the Arabic letter ه haʾ Both Latin letter e and Arabic letter ه haʾ are descendants of Phoenician letter nbsp he imaginary unit i displaystyle i nbsp nbsp ت From ت taʾ which is in turn derived from the first letter of the second word of وحدة تخيلية waḥdaẗun taḫiliyya imaginary unit pi p displaystyle pi nbsp nbsp ط From ط ṭaʾ also p displaystyle pi nbsp in some regions radius r displaystyle r nbsp nbsp نٯ From ن nun followed by a dotless ق qaf which is in turn derived from نصف القطر nuṣfu l quṭr radius kilogram kg nbsp كجم From كجم kaf jim mim In some regions alternative symbols like nbsp كغ kaf ġayn or nbsp كلغ kaf lam ġayn are used All three abbreviations are derived from كيلوغرام kiluġram kilogram and its variant spellings gram g nbsp جم From جم jim mim which is in turn derived from جرام jram a variant spelling of غرام ġram gram meter m nbsp م From م mim which is in turn derived from متر mitr meter centimeter cm nbsp سم From سم sin mim which is in turn derived from سنتيمتر centimeter millimeter mm nbsp مم From مم mim mim which is in turn derived from مليمتر millimitr millimeter kilometer km nbsp كم From كم kaf mim also nbsp كلم kaf lam mim in some regions both are derived from كيلومتر kilumitr kilometer second s nbsp ث From ث ṯaʾ which is in turn derived from ثانية ṯaniya second minute min nbsp د From د dalʾ which is in turn derived from دقيقة daqiqa minute also nbsp ٯ i e dotless ق qaf in some regions hour h nbsp س From س sinʾ which is in turn derived from ساعة saʿa hour kilometer per hour km h nbsp كم س From the symbols for kilometer and hour degree Celsius C nbsp س From س sin which is in turn derived from the second word of درجة سيلسيوس darajat silsius degree Celsius also nbsp م from م mimʾ which is in turn derived from the first letter of the third word of درجة حرارة مئوية degree centigrade degree Fahrenheit F nbsp ف From ف faʾ which is in turn derived from the second word of درجة فهرنهايت darajat fahranhayt degree Fahrenheit millimeters of mercury mmHg nbsp مم ز From مم ز mim mim zayn which is in turn derived from the initial letters of the words مليمتر زئبق millimeters of mercury Angstrom A nbsp أ From أ ʾalif with hamzah and ring above which is in turn derived from the first letter of Angstrom variously spelled أنغستروم or أنجستروم Sets and number systems edit Description Latin Arabic Notes Natural numbers N displaystyle mathbb N nbsp nbsp ط From ط ṭaʾ which is in turn derived from the first letter of the second word of عدد طبيعي ʿadadun ṭabiʿiyyun natural number Integers Z displaystyle mathbb Z nbsp nbsp ص From ص ṣad which is in turn derived from the first letter of the second word of عدد صحيح ʿadadun ṣaḥiḥun integer Rational numbers Q displaystyle mathbb Q nbsp nbsp ن From ن nun which is in turn derived from the first letter of نسبة nisba ratio Real numbers R displaystyle mathbb R nbsp nbsp ح From ح ḥaʾ which is in turn derived from the first letter of the second word of عدد حقيقي ʿadadun ḥaqiqiyyun real number Imaginary numbers I displaystyle mathbb I nbsp nbsp ت From ت taʾ which is in turn derived from the first letter of the second word of عدد تخيلي ʿadadun taḫiliyyun imaginary number Complex numbers C displaystyle mathbb C nbsp nbsp م From م mim which is in turn derived from the first letter of the second word of عدد مركب ʿadadun murakkabun complex number Empty set displaystyle varnothing nbsp displaystyle varnothing nbsp Is an element of displaystyle in nbsp displaystyle ni nbsp A mirrored Subset displaystyle subset nbsp displaystyle supset nbsp A mirrored Superset displaystyle supset nbsp displaystyle subset nbsp A mirrored Universal set S displaystyle mathbf S nbsp nbsp ش From ش sin which is in turn derived from the first letter of the second word of مجموعة شاملة majmuʿatun samila universal set Arithmetic and algebra edit Description Latin Greek Arabic Notes Percent nbsp e g 100 ١٠٠ Permille nbsp is an Arabic equivalent of the per ten thousand sign Is proportional to displaystyle propto nbsp nbsp A mirrored n th root n displaystyle sqrt n nbsp nbsp ں ں is a dotless ن nun while is a mirrored radical sign Logarithm log displaystyle log nbsp nbsp لو From لو lam waw which is in turn derived from لوغاريتم luġaritm logarithm Logarithm to base b log b displaystyle log b nbsp nbsp لوٮ Natural logarithm ln displaystyle ln nbsp nbsp لوھ From the symbols of logarithm and Euler s number Summation displaystyle sum nbsp nbsp مجــــ مجـــ mim medial form of jim is derived from the first two letters of مجموع majmuʿ sum also nbsp a mirrored summation sign in some regions Product displaystyle prod nbsp nbsp جــــذ From جذ jim ḏal The Arabic word for product is جداء jadaʾun Also displaystyle prod nbsp in some regions Factorial n displaystyle n nbsp nbsp ں Also nbsp ں in some regions Permutations n P r displaystyle n mathbf P r nbsp nbsp ںلر Also nbsp ل ں ر is used in some regions as P n r displaystyle mathbf P n r nbsp Combinations n C k displaystyle n mathbf C k nbsp nbsp ںٯك Also nbsp ٯ ں ك is used in some regions as C n k displaystyle mathbf C n k nbsp and nbsp ںك as the binomial coefficient n k displaystyle n choose k nbsp Trigonometric and hyperbolic functions edit Trigonometric functions edit Description Latin Arabic Notes Sine sin displaystyle sin nbsp nbsp حا from حاء ḥaʾ i e dotless ج jim ʾalif also nbsp جب jim baʾ is used in some regions e g Syria Arabic for sine is جيب jayb Cosine cos displaystyle cos nbsp nbsp حتا from حتا ḥaʾ i e dotless ج jim taʾ ʾalif also nbsp تجب taʾ jim baʾ is used in some regions e g Syria Arabic for cosine is جيب تمام Tangent tan displaystyle tan nbsp nbsp طا from طا ṭaʾ i e dotless ظ ẓaʾ ʾalif also nbsp ظل ẓaʾ lam is used in some regions e g Syria Arabic for tangent is ظل ẓill Cotangent cot displaystyle cot nbsp nbsp طتا from طتا ṭaʾ i e dotless ظ ẓaʾ taʾ ʾalif also nbsp تظل taʾ ẓaʾ lam is used in some regions e g Syria Arabic for cotangent is ظل تمام Secant sec displaystyle sec nbsp nbsp ٯا from ٯا dotless ق qaf ʾalif Arabic for secant is قاطع Cosecant csc displaystyle csc nbsp nbsp ٯتا from ٯتا dotless ق qaf taʾ ʾalif Arabic for cosecant is قاطع تمام Hyperbolic functions edit The letter nbsp 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 h displaystyle operatorname h nbsp is added to the end of trigonometric functions in Latin based notation nbsp Description Hyperbolic sine Hyperbolic cosine Hyperbolic tangent Hyperbolic cotangent Hyperbolic secant Hyperbolic cosecant Latin sinh displaystyle sinh nbsp cosh displaystyle cosh nbsp tanh displaystyle tanh nbsp coth displaystyle coth nbsp sech displaystyle operatorname sech nbsp csch displaystyle operatorname csch nbsp Arabic حاز حتاز طاز طتاز ٯاز ٯتاز Inverse trigonometric functions edit For inverse trigonometric functions the superscript ١ in Arabic notation is similar in usage to the superscript 1 displaystyle 1 nbsp in Latin based notation nbsp Description Inverse sine Inverse cosine Inverse tangent Inverse cotangent Inverse secant Inverse cosecant Latin sin 1 displaystyle sin 1 nbsp cos 1 displaystyle cos 1 nbsp tan 1 displaystyle tan 1 nbsp cot 1 displaystyle cot 1 nbsp sec 1 displaystyle sec 1 nbsp csc 1 displaystyle csc 1 nbsp Arabic حا ١ حتا ١ طا ١ طتا ١ ٯا ١ ٯتا ١ Inverse hyperbolic functions edit nbsp Description Inverse hyperbolic sine Inverse hyperbolic cosine Inverse hyperbolic tangent Inverse hyperbolic cotangent Inverse hyperbolic secant Inverse hyperbolic cosecant Latin sinh 1 displaystyle sinh 1 nbsp cosh 1 displaystyle cosh 1 nbsp tanh 1 displaystyle tanh 1 nbsp coth 1 displaystyle coth 1 nbsp sech 1 displaystyle operatorname sech 1 nbsp csch 1 displaystyle operatorname csch 1 nbsp Arabic حاز ١ حتاز ١ طاز ١ طتاز ١ ٯاز ١ ٯتاز ١ Calculus edit Description Latin Arabic Notes Limit lim displaystyle lim nbsp nbsp نهــــا نهــــا nun haʾ ʾalif is derived from the first three letters of Arabic نهاية nihaya limit Function f x displaystyle mathbf f x nbsp nbsp د س د dal is derived from the first letter of دالة function Also called تابع تا for short in some regions Derivatives f x d y d x d 2 y d x 2 y x displaystyle mathbf f x dfrac dy dx dfrac d 2 y dx 2 dfrac partial y partial x nbsp nbsp ص س د٢ص د س٢ د ص د س س د is a mirrored prime while is an Arabic comma The signs should be mirrored Integrals displaystyle int iint iiint oint nbsp nbsp Mirrored and Complex analysis edit Latin Greek Arabic z x i y r cos f i sin f r e i f r f displaystyle z x iy r cos varphi i sin varphi re i varphi r angle varphi nbsp nbsp ع س ت ص ل حتا ى ت حا ى ل ھت ى ل ىSee also editMathematical notation Arabic Mathematical Alphabetic SymbolsReferences edit Moore Terry Why is X the Unknown Ted Talk Archived from the original on 2014 02 22 Retrieved 2012 10 11 Cajori Florian 1993 A History of Mathematical Notation Courier Dover Publications pp 382 383 ISBN 9780486677668 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 editMultilingual mathematical e document processing Arabic mathematical notation W3C Interest Group Note Arabic math editor by WIRIS Retrieved from https en wikipedia org w index php title Modern Arabic mathematical notation amp oldid 1218970593, wikipedia, wiki, book, books, library,
