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Mathematics during the
Golden Age of Islam The Islamic Golden Age was a period of cultural, economic, and scientific flourishing in the history of Islam, traditionally dated from the 8th century to the 14th century. This period is traditionally understood to have begun during the reign ...
, especially during the 9th and 10th centuries, was built on
Greek mathematics Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathe ...
(
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Elements'' treatise, which established the foundations of ge ...
,
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists i ...
, Apollonius) and
Indian mathematics Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, ...
(
Aryabhata Aryabhata (ISO: ) or Aryabhata I (476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the '' Aryabhatiya'' (which ...
,
Brahmagupta Brahmagupta ( – ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical tr ...
). Important progress was made, such as full development of the decimal
place-value system Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...
to include
decimal fractions The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
, the first systematised study of
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...
, and advances in
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
and
trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...
. Arabic works played an important role in the transmission of mathematics to Europe during the 10th—12th centuries.


Concepts


Algebra

The study of
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...
, the name of which is derived from the
Arabic Arabic (, ' ; , ' or ) is a Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C. E.Watson; Walte ...
word meaning completion or "reunion of broken parts", flourished during the
Islamic golden age The Islamic Golden Age was a period of cultural, economic, and scientific flourishing in the history of Islam, traditionally dated from the 8th century to the 14th century. This period is traditionally understood to have begun during the reign ...
.
Muhammad ibn Musa al-Khwarizmi Muḥammad ibn Mūsā al-Khwārizmī ( ar, محمد بن موسى الخوارزمي, Muḥammad ibn Musā al-Khwārazmi; ), or al-Khwarizmi, was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astronom ...
, a Persian scholar in the
House of Wisdom The House of Wisdom ( ar, بيت الحكمة, Bayt al-Ḥikmah), also known as the Grand Library of Baghdad, refers to either a major Abbasid public academy and intellectual center in Baghdad or to a large private library belonging to the Abba ...
in
Baghdad Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesiphon ...
was the founder of algebra, is along with the
Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...
mathematician
Diophantus Diophantus of Alexandria ( grc, Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the aut ...
, known as the father of algebra. In his book ''
The Compendious Book on Calculation by Completion and Balancing ''The Compendious Book on Calculation by Completion and Balancing'' ( ar, كتاب المختصر في حساب الجبر والمقابلة, ; la, Liber Algebræ et Almucabola), also known as ''Al-Jabr'' (), is an Arabic mathematical treati ...
'', Al-Khwarizmi deals with ways to solve for the
positive Positive is a property of positivity and may refer to: Mathematics and science * Positive formula, a logical formula not containing negation * Positive number, a number that is greater than 0 * Plus sign, the sign "+" used to indicate a posi ...
root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the sur ...
s of first and second degree (linear and quadratic)
polynomial equations In mathematics, an algebraic equation or polynomial equation is an equation of the form :P = 0 where ''P'' is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term ''algebraic equation'' ...
. He introduces the method of reduction, and unlike Diophantus, also gives general solutions for the equations he deals with. Al-Khwarizmi's algebra was rhetorical, which means that the equations were written out in full sentences. This was unlike the algebraic work of Diophantus, which was syncopated, meaning that some symbolism is used. The transition to symbolic algebra, where only symbols are used, can be seen in the work of
Ibn al-Banna' al-Marrakushi Ibn al‐Bannāʾ al‐Marrākushī ( ar, ابن البناء المراكشي), full name: Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi al-Marrakushi () (29 December 1256 – 31 July 1321), was a Moroccan polymath who was active as a math ...
and Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī. On the work done by Al-Khwarizmi, J. J. O'Connor and
Edmund F. Robertson Edmund Frederick Robertson (born 1 June 1943) is a professor emeritus of pure mathematics at the University of St Andrews. Work Robertson is one of the creators of the MacTutor History of Mathematics archive, along with John J. O'Connor. Ro ...
said: Several other mathematicians during this time period expanded on the algebra of Al-Khwarizmi. Abu Kamil Shuja' wrote a book of algebra accompanied with geometrical illustrations and proofs. He also enumerated all the possible solutions to some of his problems.
Abu al-Jud Abū al-Jūd Muḥammad b. Aḥmad b. al-Layth was an Iranian mathematician. He lived during 10th century and was a contemporary of Al-Biruni. Not much is known about his life. He seems to have lived in the east of Khurasan, within Samanid territor ...
,
Omar Khayyam Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīsābūrī (18 May 1048 – 4 December 1131), commonly known as Omar Khayyam ( fa, عمر خیّام), was a polymath, known for his contributions to mathematics, astronomy, philosophy, a ...
, along with
Sharaf al-Dīn al-Tūsī Sharaf al-Dīn al-Muẓaffar ibn Muḥammad ibn al-Muẓaffar al-Ṭūsī ( fa, شرف‌الدین مظفر بن محمد بن مظفر توسی; 1135 – 1213) was an Iranian mathematician and astronomer of the Islamic Golden Age (during the ...
, found several solutions of the
cubic equation In algebra, a cubic equation in one variable is an equation of the form :ax^3+bx^2+cx+d=0 in which is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of th ...
. Omar Khayyam found the general geometric solution of a cubic equation.


Cubic equations

Omar Khayyam Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīsābūrī (18 May 1048 – 4 December 1131), commonly known as Omar Khayyam ( fa, عمر خیّام), was a polymath, known for his contributions to mathematics, astronomy, philosophy, a ...
(c. 1038/48 in
Iran Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkme ...
– 1123/24) wrote the ''Treatise on Demonstration of Problems of Algebra'' containing the systematic solution of cubic or third-order equations, going beyond the ''Algebra'' of al-Khwārizmī. Khayyám obtained the solutions of these equations by finding the intersection points of two
conic section In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a speci ...
s. This method had been used by the Greeks, but they did not generalize the method to cover all equations with positive roots.
Sharaf al-Dīn al-Ṭūsī Sharaf al-Dīn al-Muẓaffar ibn Muḥammad ibn al-Muẓaffar al-Ṭūsī ( fa, شرف‌الدین مظفر بن محمد بن مظفر توسی; 1135 – 1213) was an Iranian mathematician and astronomer of the Islamic Golden Age (during th ...
(? in
Tus, Iran Tus (Persian: توس Tus), also spelled as Tous or Toos, is an ancient city in Razavi Khorasan Province in Iran near Mashhad. To the ancient Greeks, it was known as Susia ( grc, Σούσια). It was also known as Tusa. Tus was divided into ...
– 1213/4) developed a novel approach to the investigation of cubic equations—an approach which entailed finding the point at which a cubic polynomial obtains its maximum value. For example, to solve the equation \ x^3 + a = b x, with ''a'' and ''b'' positive, he would note that the maximum point of the curve \ y = b x - x^3 occurs at x = \textstyle\sqrt, and that the equation would have no solutions, one solution or two solutions, depending on whether the height of the curve at that point was less than, equal to, or greater than ''a''. His surviving works give no indication of how he discovered his formulae for the maxima of these curves. Various conjectures have been proposed to account for his discovery of them.


Induction

The earliest implicit traces of mathematical induction can be found in
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Elements'' treatise, which established the foundations of ge ...
's proof that the number of primes is infinite (c. 300 BCE). The first explicit formulation of the principle of induction was given by Pascal in his ''Traité du triangle arithmétique'' (1665). In between, implicit
proof Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a co ...
by induction for arithmetic sequences was introduced by al-Karaji (c. 1000) and continued by
al-Samaw'al Al-Samawʾal ibn Yaḥyā al-Maghribī ( ar, السموأل بن يحيى المغربي, ; c. 1130 – c. 1180), commonly known as Samau'al al-Maghribi, was a mathematician, astronomer and physician. Born to a Jewish family, he concealed his con ...
, who used it for special cases of the
binomial theorem In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where the ...
and properties of
Pascal's triangle In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although ...
.


Irrational numbers

The Greeks had discovered
irrational number In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two inte ...
s, but were not happy with them and only able to cope by drawing a distinction between ''magnitude'' and ''number''. In the Greek view, magnitudes varied continuously and could be used for entities such as line segments, whereas numbers were discrete. Hence, irrationals could only be handled geometrically; and indeed Greek mathematics was mainly geometrical. Islamic mathematicians including Abū Kāmil Shujāʿ ibn Aslam and Ibn Tahir al-Baghdadi slowly removed the distinction between magnitude and number, allowing irrational quantities to appear as coefficients in equations and to be solutions of algebraic equations. They worked freely with irrationals as mathematical objects, but they did not examine closely their nature. In the twelfth century,
Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
translations of
Al-Khwarizmi Muḥammad ibn Mūsā al-Khwārizmī ( ar, محمد بن موسى الخوارزمي, Muḥammad ibn Musā al-Khwārazmi; ), or al-Khwarizmi, was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astronom ...
's
Arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th c ...
on the
Indian numerals Indian or Indians may refer to: Peoples South Asia * Indian people, people of Indian nationality, or people who have an Indian ancestor ** Non-resident Indian, a citizen of India who has temporarily emigrated to another country * South Asia ...
introduced the
decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
positional number system Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...
to the
Western world The Western world, also known as the West, primarily refers to the various nations and states in the regions of Europe, North America, and Oceania.
. His ''Compendious Book on Calculation by Completion and Balancing'' presented the first systematic solution of
linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...
and
quadratic equation In algebra, a quadratic equation () is any equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where represents an unknown value, and , , and represent known numbers, where . (If and then the equation is linear, not quadr ...
s. In
Renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ideas ...
Europe, he was considered the original inventor of algebra, although it is now known that his work is based on older Indian or Greek sources. He revised
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
's ''
Geography Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and ...
'' and wrote on astronomy and astrology. However, C.A. Nallino suggests that al-Khwarizmi's original work was not based on Ptolemy but on a derivative world map, presumably in
Syriac Syriac may refer to: *Syriac language, an ancient dialect of Middle Aramaic *Sureth, one of the modern dialects of Syriac spoken in the Nineveh Plains region * Syriac alphabet ** Syriac (Unicode block) ** Syriac Supplement * Neo-Aramaic languages ...
or
Arabic Arabic (, ' ; , ' or ) is a Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C. E.Watson; Walte ...
.


Spherical trigonometry

The spherical
law of sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, \frac \,=\, \frac \,=\, \frac \,=\, 2R, where , and ar ...
was discovered in the 10th century: it has been attributed variously to Abu-Mahmud Khojandi,
Nasir al-Din al-Tusi Muhammad ibn Muhammad ibn al-Hasan al-Tūsī ( fa, محمد ابن محمد ابن حسن طوسی 18 February 1201 – 26 June 1274), better known as Nasir al-Din al-Tusi ( fa, نصیر الدین طوسی, links=no; or simply Tusi in the West ...
and
Abu Nasr Mansur Abu Nasri Mansur ibn Ali ibn Iraq ( fa, أبو نصر منصور بن علی بن عراق; c. 960 – 1036) was a Persian Muslim mathematician and astronomer. He is well known for his work with the spherical sine law.Bijli suggests that three ...
, with
Abu al-Wafa' Buzjani Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī ( fa, ابوالوفا بوزجانی or بوژگانی) (10 June 940 – 15 July 998) was a Persian mathematician ...
as a contributor. Ibn Muʿādh al-Jayyānī's ''The book of unknown arcs of a sphere'' in the 11th century introduced the general law of sines. The plane law of sines was described in the 13th century by
Nasīr al-Dīn al-Tūsī Muhammad ibn Muhammad ibn al-Hasan al-Tūsī ( fa, محمد ابن محمد ابن حسن طوسی 18 February 1201 – 26 June 1274), better known as Nasir al-Din al-Tusi ( fa, نصیر الدین طوسی, links=no; or simply Tusi in the West ...
. In his ''On the Sector Figure'', he stated the law of sines for plane and spherical triangles and provided proofs for this law.


Negative numbers

In the 9th century, Islamic mathematicians were familiar with negative numbers from the works of Indian mathematicians, but the recognition and use of negative numbers during this period remained timid.
Al-Khwarizmi Muḥammad ibn Mūsā al-Khwārizmī ( ar, محمد بن موسى الخوارزمي, Muḥammad ibn Musā al-Khwārazmi; ), or al-Khwarizmi, was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astronom ...
did not use negative numbers or negative coefficients. But within fifty years, Abu Kamil illustrated the rules of signs for expanding the multiplication (a \pm b)(c \pm d). Al-Karaji wrote in his book ''al-Fakhrī'' that "negative quantities must be counted as terms". In the 10th century,
Abū al-Wafā' al-Būzjānī Abū al-Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī ( fa, ابوالوفا بوزجانی or بوژگانی) (10 June 940 – 15 July 998) was a Persian mathematician a ...
considered debts as negative numbers in ''A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen''. By the 12th century, al-Karaji's successors were to state the general rules of signs and use them to solve
polynomial division In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, beca ...
s. As
al-Samaw'al Al-Samawʾal ibn Yaḥyā al-Maghribī ( ar, السموأل بن يحيى المغربي, ; c. 1130 – c. 1180), commonly known as Samau'al al-Maghribi, was a mathematician, astronomer and physician. Born to a Jewish family, he concealed his con ...
writes:
the product of a negative number — ''al-nāqiṣ'' — by a positive number — ''al-zāʾid'' — is negative, and by a negative number is positive. If we subtract a negative number from a higher negative number, the remainder is their negative difference. The difference remains positive if we subtract a negative number from a lower negative number. If we subtract a negative number from a positive number, the remainder is their positive sum. If we subtract a positive number from an empty power (''martaba khāliyya''), the remainder is the same negative, and if we subtract a negative number from an empty power, the remainder is the same positive number.


Double false position

Between the 9th and 10th centuries, the Egyptian mathematician Abu Kamil wrote a now-lost treatise on the use of double false position, known as the ''Book of the Two Errors'' (''Kitāb al-khaṭāʾayn''). The oldest surviving writing on double false position from the
Middle East The Middle East ( ar, الشرق الأوسط, ISO 233: ) is a geopolitical region commonly encompassing Arabia (including the Arabian Peninsula and Bahrain), Asia Minor (Asian part of Turkey except Hatay Province), East Thrace (Europea ...
is that of
Qusta ibn Luqa Qusta ibn Luqa (820–912) (Costa ben Luca, Constabulus) was a Syrian Melkite Christian physician, philosopher, astronomer, mathematician and translator. He was born in Baalbek. Travelling to parts of the Byzantine Empire, he brought back Greek ...
(10th century), an
Arab The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, No ...
mathematician from
Baalbek Baalbek (; ar, بَعْلَبَكّ, Baʿlabakk, Syriac-Aramaic: ܒܥܠܒܟ) is a city located east of the Litani River in Lebanon's Beqaa Valley, about northeast of Beirut. It is the capital of Baalbek-Hermel Governorate. In Greek and Roma ...
,
Lebanon Lebanon ( , ar, لُبْنَان, translit=lubnān, ), officially the Republic of Lebanon () or the Lebanese Republic, is a country in Western Asia. It is located between Syria to the north and east and Israel to the south, while Cyprus li ...
. He justified the technique by a formal, Euclidean-style geometric proof. Within the tradition of Golden Age Muslim mathematics, double false position was known as ''hisāb al-khaṭāʾayn'' ("reckoning by two errors"). It was used for centuries to solve practical problems such as commercial and juridical questions (estate partitions according to rules of Quranic inheritance), as well as purely recreational problems. The algorithm was often memorized with the aid of
mnemonics A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imager ...
, such as a verse attributed to Ibn al-Yasamin and balance-scale diagrams explained by
al-Hassar Al-Hassar or Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar ( ar, أبو بكر محمد ابن عياش الحصَار) was a 12th-century Moroccan mathematician. He is the author of two books ''Kitab al-bayan wat-tadhkar'' (Book of Demonstr ...
and
Ibn al-Banna Ibn al‐Bannāʾ al‐Marrākushī ( ar, ابن البناء المراكشي), full name: Abu'l-Abbas Ahmad ibn Muhammad ibn Uthman al-Azdi al-Marrakushi () (29 December 1256 – 31 July 1321), was a Moroccan polymath who was active as a math ...
, who were each mathematicians of Moroccan origin.


Other major figures

Sally P. Ragep, a historian of science in Islam, estimated in 2019 that "tens of thousands" of Arabic manuscripts in mathematical sciences and philosophy remain unread, which give studies which "reflect individual biases and a limited focus on a relatively few texts and scholars"."Science Teaching in Pre-Modern Societies"
in Film Screening and Panel Discussion, ''McGill University'', 15 January 2019.
*
'Abd al-Hamīd ibn Turk ( fl. 830), known also as ( ar, ابومحمد عبدالحمید بن واسع بن ترک الجیلی) was a ninth-century Muslim mathematician. Not much is known about his life. The two records of him, one by Ibn Nadim and the other by al- ...
(fl. 830) (quadratics) *
Thabit ibn Qurra Thabit ( ar, ) is an Arabic name for males that means "the imperturbable one". It is sometimes spelled Thabet. People with the patronymic * Ibn Thabit, Libyan hip-hop musician * Asim ibn Thabit, companion of Muhammad * Hassan ibn Sabit (died 674 ...
(826–901) *
Sind ibn Ali Abu al-Tayyib Sanad ibn Ali al-Yahudi (died c. 864 C.E.), was a ninth-century Iraqi Jewish astronomer, translator, mathematician and engineer employed at the court of the Abbasid caliph Al-Ma'mun. A later convert to Islam, Sanad's father was a le ...
(d. after 864) *
Ismail al-Jazari Badīʿ az-Zaman Abu l-ʿIzz ibn Ismāʿīl ibn ar-Razāz al-Jazarī (1136–1206, ar, بديع الزمان أَبُ اَلْعِزِ إبْنُ إسْماعِيلِ إبْنُ الرِّزاز الجزري, ) was a polymath: a schola ...
(1136–1206) *
Abū Sahl al-Qūhī (; fa, ابوسهل بیژن کوهی ''Abusahl Bijan-e Koohi'') was a Persian mathematician, physicist and astronomer. He was from Kuh (or Quh), an area in Tabaristan, Amol, and flourished in Baghdad in the 10th century. He is considered one of ...
(c. 940–1000) (centers of gravity) *
Abu'l-Hasan al-Uqlidisi Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi ( ar, أبو الحسن أحمد بن ابراهيم الإقليدسي) was a Muslim Arab mathematician, who was active in Damascus and Baghdad. He wrote the earliest surviving book on the positional use ...
(952–953) (arithmetic) * 'Abd al-'Aziz al-Qabisi (d. 967) *
Ibn al-Haytham Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...
(c. 965–1040) * Abū al-Rayḥān al-Bīrūnī (973–1048) (trigonometry) *
Ibn Maḍāʾ Abu al-Abbas Ahmad bin Abd al-Rahman bin Muhammad bin Sa'id bin Harith bin Asim al-Lakhmi al-Qurtubi, better known as Ibn Maḍāʾ ( ar, ابن مضاء; 1116–1196) was an Arab Muslim polymath from Córdoba in Islamic Spain.Kees Versteegh, ...
(c. 1116–1196) *
Jamshīd al-Kāshī Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī) ( fa, غیاث الدین جمشید کاشانی ''Ghiyās-ud-dīn Jamshīd Kāshānī'') (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronome ...
(c. 1380–1429) (decimals and estimation of the circle constant)


Gallery

File:Gravure originale du compas parfait par Abū Sahl al-Qūhī.jpg, Engraving of
Abū Sahl al-Qūhī (; fa, ابوسهل بیژن کوهی ''Abusahl Bijan-e Koohi'') was a Persian mathematician, physicist and astronomer. He was from Kuh (or Quh), an area in Tabaristan, Amol, and flourished in Baghdad in the 10th century. He is considered one of ...
's perfect compass to draw conic sections. File:Theorem of al-Haitham.JPG, The theorem of Ibn Haytham.


See also

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Arabic numerals Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers such as ...
* Indian influence on Islamic mathematics in medieval Islam *
History of calculus Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, a ...
*
History of geometry Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the st ...
*
Science in the medieval Islamic world Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Umayyads of Córdoba, the Abbadids of Seville, the Samanids, the Ziyarids, the Buyids in Persia, the Abbasid Caliphate and ...
* Timeline of science and engineering in the Muslim world


References


Sources

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Further reading

;Books on Islamic mathematics * ** Review: ** Review: * * * * Sowjetische Beiträge zur Geschichte der Naturwissenschaft pp. 62–160. * ; Book chapters on Islamic mathematics * ; Books on Islamic science * * ; Books on the history of mathematics * (Reviewed: ) * ;Journal articles on Islamic mathematics * Høyrup, Jens
“The Formation of «Islamic Mathematics»: Sources and Conditions”
''Filosofi og Videnskabsteori på Roskilde Universitetscenter''. 3. Række: ''Preprints og Reprints'' 1987 Nr. 1. ;Bibliographies and biographies * Brockelmann, Carl. ''Geschichte der Arabischen Litteratur''. 1.–2. Band, 1.–3. Supplementband. Berlin: Emil Fischer, 1898, 1902; Leiden: Brill, 1937, 1938, 1942. * * * ; Television documentaries *
Marcus du Sautoy Marcus Peter Francis du Sautoy (; born 26 August 1965) is a British mathematician, Simonyi Professor for the Public Understanding of Science at the University of Oxford, Fellow of New College, Oxford and author of popular mathematics and pop ...
(presenter) (2008). "The Genius of the East". '' The Story of Maths''.
BBC #REDIRECT BBC Here i going to introduce about the best teacher of my life b BALAJI sir. He is the precious gift that I got befor 2yrs . How has helped and thought all the concept and made my success in the 10th board exam. ...
. *
Jim Al-Khalili Jameel Sadik "Jim" Al-Khalili ( ar, جميل صادق الخليلي; born 20 September 1962) is an Iraqi-British theoretical physicist, author and broadcaster. He is professor of theoretical physics and chair in the public engagement in scien ...
(presenter) (2010). '' Science and Islam''.
BBC #REDIRECT BBC Here i going to introduce about the best teacher of my life b BALAJI sir. He is the precious gift that I got befor 2yrs . How has helped and thought all the concept and made my success in the 10th board exam. ...
.


External links

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Richard Covington, ''Rediscovering Arabic Science'', 2007, Saudi Aramco WorldList of Inventions and Discoveries in Mathematics During the Islamic Golden Age
{{DEFAULTSORT:Mathematics In Medieval Islam Islamic Golden Age