MODERN ARABIC MATHEMATICAL NOTATION is a mathematical notation based
on the
CONTENTS * 1 Features * 2 Variations * 2.1 Numeral systems * 2.2 Mirrored Latin symbols * 3 Examples * 3.1 Mathematical letters
* 3.2
* 3.5 Trigonometric and hyperbolic functions * 3.5.1
* 3.6
* 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
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. * "
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
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
MIRRORED LATIN SYMBOLS Sometimes, symbols used in Arabic mathematical notation differ according to the region: LATIN ARABIC PERSIAN lim x→∞ x4 نهــــــــــــا س←∞ س٤ حــــــــــــد س←∞ س۴ * ^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): LATIN ARABIC MIRRORED LATIN n ∑ x=0 3√x ں مجــــــــــــ س=٠ ٣√س ں∑س=0 3√س * ^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 LATIN ARABIC NOTES a {displaystyle a} ا
From the Arabic letter ا ʾalif; a and ا ʾalif are the
first letters of the
b {displaystyle b} ٮ
A dotless ب bāʾ; b and ب bāʾ are the second letters of
the
c {displaystyle c} حــــ From the initial form of ح ḥāʾ, or that of a dotless ج ǧīm; c and ج ǧīm are the third letters of the Latin alphabet and the ʾabjadī sequence respectively d {displaystyle d} د
From the Arabic letter د dāl; d and د dāl are the fourth
letters of the
x {displaystyle x} 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) , meaning thing. (X was used in old Spanish for the sound /ʃ/ ). However, according to others there is no historical evidence for this. y {displaystyle y} ص From the Arabic letter ص ṣād z {displaystyle z} ع From the Arabic letter ع ʿayn MATHEMATICAL CONSTANTS AND UNITS DESCRIPTION LATIN ARABIC NOTES Euler\'s number e {displaystyle e} ھ Initial form of the Arabic letter ه hāʾ. Both Latin letter e and Arabic letter ه hāʾ are descendants of Phoenician letter hē. imaginary unit i {displaystyle i} ت From ت tāʾ, which is in turn derived from the first letter of the second word of وحدة تخيلية waḥdaẗun taḫīliyya "imaginary unit" pi {displaystyle pi } ط From ط ṭāʾ; also {displaystyle pi } in some regions radius r {displaystyle r} نٯ From ن nūn followed by a dotless ق qāf, which is in turn derived from نصف القطر nuṣfu l-quṭr "radius" kilogram kg كجم From كجم kāf-ǧīm-mīm. In some regions alternative symbols like ( كغ kāf-ġayn) or ( كغم kāf-ġayn-mīm) are used. All three abbreviations are derived from كيلوغرام kīlūġrām "kilogram" and its variant spellings. gram g جم From جم ǧīm-mīm, which is in turn derived from جرام ǧrām, a variant spelling of غرام ġrām "gram" meter m م From م mīm, which is in turn derived from متر mitr "meter" centimeter cm سم From سم sīn-mīm, which is in turn derived from سنتيمتر "centimeter" millimeter mm مم From مم mīm-mīm, which is in turn derived from مليمتر millīmitr "millimeter" kilometer km كم From كم kāf-mīm; also ( كلم kāf-lām-mīm) in some regions; both are derived from كيلومتر kīlūmitr "kilometer". second s ث From ث ṯāʾ, which is in turn derived from ثانية ṯāniya "second" minute min د From د dālʾ, which is in turn derived from دقيقة daqīqa "minute"; also ( ٯ , i.e. dotless ق qāf) in some regions hour h س From س sīnʾ, which is in turn derived from ساعة sāʿa "hour" kilometer per hour km/h كم/س From the symbols for kilometer and hour degree Celsius °C °س 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" degree Fahrenheit °F °ف From ف fāʾ, which is in turn derived from the second word of درجة فهرنهايت darajat fahranhāyt "degree Fahrenheit" millimeters of mercury mmHg ممز From ممز mīm-mīm zayn, which is in turn derived from the initial letters of the words مليمتر زئبق "millimeters of mercury" أْ 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 DESCRIPTION LATIN ARABIC NOTES
ط From ط ṭāʾ, which is in turn derived from the first letter of the second word of عدد طبيعيʿadadun ṭabīʿiyyun "natural number"
ص From ص ṣād, which is in turn derived from the first letter of the second word of عدد صحيح ʿadadun ṣaḥīḥun "integer"
ن From ن nūn, which is in turn derived from the first letter of نسبة nisba "ratio"
ح From ح ḥāʾ, which is in turn derived from the first letter of the second word of عدد حقيقي ʿadadun ḥaqīqiyyun "real number"
ت From ت tāʾ, which is in turn derived from the first letter of the second word of عدد تخيلي ʿadadun taḫīliyyun "imaginary number"
م 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 {displaystyle in } {displaystyle ni } ∈ A mirrored ∈
ش From ش šīn, which is in turn derived from the first letter of the second word of مجموعة شاملة maǧmūʿaẗun šāmila "universal set" ARITHMETIC AND ALGEBRA DESCRIPTION LATIN ARABIC NOTES ٪ e.g. 100% "٪١٠٠"
؉ ؊ is an Arabic equivalent of the per ten thousand sign ‱. Is proportional to {displaystyle propto } ∝ A mirrored ∝ n th root n {displaystyle {sqrt{,,,}}} ں√ ں is a dotless ن nūn while √ is a mirrored radical sign √
لو From لو lām-wāw, which is in turn derived from لوغاريتم lūġārītum "logarithm"
لوٮ
لوھ From the symbols of logarithm and Euler's number
مجــــ مجـــ mīm-medial form of ǧīm is derived from the first two letters of مجموع maǧmūʿ "sum"; also (∑, a mirrored summation sign ∑) in some regions Product {displaystyle prod } جــــذ From جذ ǧīm-ḏāl. The Arabic word for "product" is جداء ǧadāʾun. Also {displaystyle prod } in some regions.
ں Also ( ں! ) in some regions
ںلر Also ( ل(ں،ر) ) is used in some regions as P ( n , r ) {displaystyle mathbf {P} (n,r)}
ںٯك Also ( ٯ(ں،ك) ) is used in some regions as C ( n , k ) {displaystyle mathbf {C} (n,k)} and ( ⎛⎝ں ك⎞⎠ ) as the binomial coefficient ( n k ) {displaystyle n choose k} TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS Trigonometric Functions DESCRIPTION LATIN ARABIC NOTES Sine sin {displaystyle sin } حا from حتا ḥāʾ (i.e. dotless ج ǧīm)-tāʾ-ʾalif; also ( جب ǧīm-bāʾ) is used in some regions (e.g. Syria); Arabic for "sine" is جيب ǧayb Cosine cos {displaystyle cos } حتا from حتا ḥāʾ (i.e. dotless ج ǧīm)-tāʾ-ʾalif; also ( تجب tāʾ-ǧīm-bāʾ) is used in some regions (e.g. Syria); Arabic for "cosine" is جيب تمام Tangent tan {displaystyle tan } طا from طا ṭāʾ (i.e. dotless ظ ẓāʾ)-tāʾ-ʾalif; also ( ظل ẓāʾ-lām) is used in some regions (e.g. Syria); Arabic for "tangent" is ظل ẓill Cotangent cot {displaystyle cot } طتا 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 Secant sec {displaystyle sec } ٯا from ٯا dotless ق qāf-ʾalif; Arabic for "secant" is أو قاطع Cosecant csc {displaystyle csc } ٯتا 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 h {displaystyle operatorname {h} } is added to the end of trigonometric functions in Latin-based notation. DESCRIPTION Hyperbolic sine Hyperbolic cosine Hyperbolic tangent Hyperbolic cotangent Hyperbolic secant Hyperbolic cosecant LATIN sinh {displaystyle sinh } cosh {displaystyle cosh } tanh {displaystyle tanh } coth {displaystyle coth } sech {displaystyle operatorname {sech} } csch {displaystyle operatorname {csch} } ARABIC حاز حتاز طاز طتاز ٯاز ٯتاز Inverse Trigonometric Functions For inverse trigonometric functions, the superscript −١ in Arabic notation is similar in usage to the superscript 1 {displaystyle -1} in Latin-based notation. DESCRIPTION Inverse sine Inverse cosine Inverse tangent Inverse cotangent Inverse secant Inverse cosecant LATIN sin 1 {displaystyle sin ^{-1}} cos 1 {displaystyle cos ^{-1}} tan 1 {displaystyle tan ^{-1}} cot 1 {displaystyle cot ^{-1}} sec 1 {displaystyle sec ^{-1}} csc 1 {displaystyle csc ^{-1}} ARABIC حا−١ حتا−١ طا−١ طتا−١ ٯا−١ ٯتا−١ Inverse Hyperbolic Functions 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}} cosh 1 {displaystyle cosh ^{-1}} tanh 1 {displaystyle tanh ^{-1}} coth 1 {displaystyle coth ^{-1}} sech 1 {displaystyle operatorname {sech} ^{-1}} csch 1 {displaystyle operatorname {csch} ^{-1}} ARABIC حاز−١ حتاز−١ طاز−١ طتاز−١ ٯاز−١ ٯتاز−١ CALCULUS DESCRIPTION LATIN ARABIC NOTES Limit lim {displaystyle lim } نهــــا نهــــا nūn-hāʾ-ʾalif is derived from the first three letters of Arabic نهاية nihāya "limit" function f ( x ) {displaystyle mathbf {f} (x)} د(س) د dāl is derived from the first letter of دالة "function" 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}}}} د‵(س)، دص/ دس ، د٢ص/ دس٢ ، ∂ص/ ∂س ‵ is a mirrored prime ′ while ، is an Arabic comma. The ∂ signs should be mirrored: ∂. Integrals , , , {displaystyle int {},iint {},iiint {},oint {}} ∫ ،∬ ،∭ ،∮ Mirrored ∫, ∬, ∭ and ∮ COMPLEX ANALYSIS LATIN ARABIC z = x + i y = r ( cos + i sin ) = r e i = 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 *
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 - by
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