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In the [[history of mathematics]], '''mathematics in medieval Islam''', often termed '''Islamic mathematics''' or '''Arabic mathematics''', covers the body of [[mathematics]] preserved and developed by the [[Muslim world|Islamic civilization]] between |
In the [[history of mathematics]], '''mathematics in medieval Islam''', often termed '''Islamic mathematics''' or '''Arabic mathematics''', covers the body of [[mathematics]] preserved and developed by the [[Muslim world|Islamic civilization]] between circa 622 and 1600.{{sfn|Hogendijk|1999}} [[Islamic science]] and mathematics flourished under the Islamic [[caliphate]] established across the Middle East, [[Central Asia]], [[North Africa]], [[Southern Italy]], the [[Iberian Peninsula]], and, at its peak, parts of France and [[Indian subcontinent|India]]. |
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Katz, in ''A history of mathematics'' says that |
Katz, in ''A history of mathematics'' says that:{{sfn|Katz|1993}} |
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<blockquote>A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied... Still, the general outline... is known. In particular, Islamic mathematicians fully developed the decimal place-value number system to include decimal fractions, systematised the study of algebra and began to consider the relationship between algebra and geometry, studied and made advances on the major Greek geometrical treatises of Euclid, Archimedes, and Apollonius, and made significant improvements in plane and spherical geometry |
<blockquote>"A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied... Still, the general outline... is known. In particular, Islamic mathematicians fully developed the decimal place-value number system to include decimal fractions, systematised the study of algebra and began to consider the relationship between algebra and geometry, studied and made advances on the major Greek geometrical treatises of Euclid, Archimedes, and Apollonius, and made significant improvements in plane and spherical geometry."</blockquote> |
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An important role was played by the translation and study of Greek mathematics, which was the principal route of transmission of these texts to Western Europe. Smith notes that |
An important role was played by the translation and study of Greek mathematics, which was the principal route of transmission of these texts to Western Europe. Smith notes that:{{sfn|Smith|1958|loc=Vol. 1, Chapter VII.4}} |
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⚫ | <blockquote>"the world owes a great debt to Arab scholars for preserving and transmitting to posterity the classics of Greek mathematics... their work was chiefly that of transmission, although they developed considerable ingenuity in algebra and showed some genius in their work in trigonometry."</blockquote> |
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⚫ | <blockquote>the world owes a great debt to Arab scholars for preserving and transmitting to posterity the classics of Greek mathematics... their work was chiefly that of transmission, although they developed considerable ingenuity in algebra and showed some genius in their work in trigonometry |
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There is some controversy as to the relative weight of ''transmission'' versus ''original work'' in the value of the medieval Islamic contribution. |
There is some controversy as to the relative weight of ''transmission'' versus ''original work'' in the value of the medieval Islamic contribution. |
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== History == |
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===== Omar Khayyám ===== |
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[[Image:Omar Kayyám - Geometric solution to cubic equation.png|thumb|To solve the third-degree equation ''x''<sup>3</sup> + ''a''<sup>2</sup>''x'' = ''b'' Khayyám constructed the [[parabola]] ''x''<sup>2</sup> = ''ay'', a [[circle]] with diameter ''b''/''a''<sup>2</sup>, and a vertical line through the intersection point. The solution is given by the length of the horizontal line segment from the origin to the intersection of the vertical line and the ''x''-axis.]] |
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[[Omar Khayyám]] (c. 1038/48–1123/24){{sfn|Struik|1987|p=96}} wrote the ''Treatise on Demonstration of Problems of Algebra'' containing the systematic solution of [[third-degree equation]]s, going beyond the ''Algebra'' of [[Muḥammad ibn Mūsā al-Khwārizmī|al-Khwārizmī]].{{sfn|Boyer|1991|pp=241–242}} Khayyám obtained the solutions of these equations by finding the [[intersection point]]s of two [[conic section]]s. This method had been used by the Greeks,{{sfn|Struik|1987|p=97}} but they did not generalize the method to cover all equations with positive [[root (equation)|root]]s.{{sfn|Boyer|19991|pp=241–242}} |
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Khayyám differentiated between "geometric" and "arithmetic" solutions.{{sfn|Struik|1987|p=97}} Khayyám mistakenly believed{{sfn|Boyer|1991|pp=241–242}} arithmetic solutions only existed if the [[root (equation)|root]]s where [[positive number|positive]] and [[rational number|rational]].{{sfn|Struik|1987|p=97}} Khayyám did not concern himself with numerical calculations of the solutions.{{sfn|Struik|1987|p=97}} |
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{{#tag:ref|"Omar Khayyam (ca. 1050–1123), the "tent-maker," wrote an ''Algebra'' that went beyond that of al-Khwarizmi to include equations of third degree. Like his Arab predecessors, Omar Khayyam provided for quadratic equations both arithmetic and geometric solutions; for general cubic equations, he believed (mistakenly, as the sixteenth century later showed), arithmetic solutions were impossible; hence he gave only geometric solutions. The scheme of using intersecting conics to solve cubics had been used earlier by Menaechmus, Archimedes, and Alhazan, but Omar Khayyam took the praiseworthy step of generalizing the method to cover all third-degree equations (having positive roots). [...] For equations of higher degree than three, Omar Khayyam evidently did not envision similar geometric methods, for space does not contain more than three dimensions, [...]"{{sfn|Boyer|1991|pp=241–242}}|group="note"}} |
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== Major figures and developments == |
== Major figures and developments == |
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* [[Jamshīd al-Kāshī]] (c. 1380 - 1429) (decimals) |
* [[Jamshīd al-Kāshī]] (c. 1380 - 1429) (decimals) |
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== |
== Notes == |
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{{reflist}} |
{{reflist|4}} |
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== References == |
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{{refbegin|2}} |
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* {{cite book|last=Boyer|year=1991|first=Carl B.|authorlink=Carl Benjamin Boyer|title=A History of Mathematics|chapter=Greek Trigonometry and Mensuration, and The Arabic Hegemony|edition=2nd|publisher=John Wiley & Sons|location=New York City|isbn=0471543977|ref=harv}} |
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* {{cite book|last=Katz|year=1993|first=Victor J.|authorlink=Victor J. Katz|title=A History of Mathematics: An Introduction|publisher=HarperCollins college publishers|isbn=0-673-38039-4|ref=harv}}. |
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* {{cite book|last=Ronan|year=1983|first=Colin A.|authorlink=Colin Ronan|title=The Cambridge Illustrated History of the World's Science|publisher=Cambridge University Press|isbn=0521258448|ref=harv}} |
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* {{cite book|last=Smith|year=1958|first=David E.|authorlink=David Eugene Smith|title=History of Mathematics|publisher=Dover Publications|isbn=0-486-20429-4|ref=harv}} |
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* {{cite book|last=Struik|year=1987|first=Dirk J.|authorlink=Dirk Jan Struik|title=A Concise History of Mathematics|edition=4th rev.|publisher=Dover Publications|isbn=0486602559|ref=harv}} |
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{{refend}} |
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== Further reading== |
== Further reading== |
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== External links == |
== External links == |
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* |
* {{cite web|last=Hogendijk|first=Jan P.|date=January 1999|year=1999|url=http://www.jphogendijk.nl/publ/Islamath.html|title=Bibliography of Mathematics in Medieval Islamic Civilization|ref=harv}} |
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* {{MacTutor|class=HistTopics|id=Arabic_mathematics|title=Arabic mathematics: forgotten brilliance?|year=1999}} |
* {{MacTutor|class=HistTopics|id=Arabic_mathematics|title=Arabic mathematics: forgotten brilliance?|year=1999}} |
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Revision as of 20:38, 15 March 2011
In the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics or Arabic mathematics, covers the body of mathematics preserved and developed by the Islamic civilization between circa 622 and 1600.[1] Islamic science and mathematics flourished under the Islamic caliphate established across the Middle East, Central Asia, North Africa, Southern Italy, the Iberian Peninsula, and, at its peak, parts of France and India.
Katz, in A history of mathematics says that:[2]
"A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied... Still, the general outline... is known. In particular, Islamic mathematicians fully developed the decimal place-value number system to include decimal fractions, systematised the study of algebra and began to consider the relationship between algebra and geometry, studied and made advances on the major Greek geometrical treatises of Euclid, Archimedes, and Apollonius, and made significant improvements in plane and spherical geometry."
An important role was played by the translation and study of Greek mathematics, which was the principal route of transmission of these texts to Western Europe. Smith notes that:[3]
"the world owes a great debt to Arab scholars for preserving and transmitting to posterity the classics of Greek mathematics... their work was chiefly that of transmission, although they developed considerable ingenuity in algebra and showed some genius in their work in trigonometry."
There is some controversy as to the relative weight of transmission versus original work in the value of the medieval Islamic contribution.
History
Omar Khayyám
![](https://upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.png/220px-Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.png)
Omar Khayyám (c. 1038/48–1123/24)[4] wrote the Treatise on Demonstration of Problems of Algebra containing the systematic solution of third-degree equations, going beyond the Algebra of al-Khwārizmī.[5] Khayyám obtained the solutions of these equations by finding the intersection points of two conic sections. This method had been used by the Greeks,[6] but they did not generalize the method to cover all equations with positive roots.[7]
Major figures and developments
- Muhammad ibn Mūsā al-Khwārizmī (c. 780 – c. 850)
- 'Abd al-Hamīd ibn Turk (fl. 830) (quadratics)
- Thabit ibn Qurra (826–901)
- Abū Kāmil Shujā ibn Aslam (c. 850 – 930) (irrationals)
- Abū Sahl al-Qūhī (c. 940–1000) (centers of gravity)
- Abu'l-Hasan al-Uqlidisi (952 – 953) (arithmetic)
- 'Abd al-'Aziz al-Qabisi
- Abū al-Wafā' Būzjānī (940 - 998) (spherical trigonometry)
- Al-Karaji (c. 953 – c. 1029) (algebra, induction)
- Abu Nasr Mansur (c. 960 – 1036) (spherical trigonometry)
- Ibn Tahir al-Baghdadi (c. 980–1037) (irrationals)
- Ibn al-Haytham (ca. 965–1040)
- Abū al-Rayḥān al-Bīrūnī (973 - 1048) (trigonometry)
- Al-Khayyam (1048 - 1131) (cubic equations, parallel postulate)
- Ibn Yaḥyā al-Maghribī al-Samawʾal (c. 1130 – c. 1180)
- Sharaf al-Dīn al-Ṭūsī (c. 1150 – 1215) (cubics)
- Naṣīr al-Dīn al-Ṭūsī (1201 - 1274) (parallel postulate)
- Jamshīd al-Kāshī (c. 1380 - 1429) (decimals)
Notes
- ^ Hogendijk 1999.
- ^ Katz 1993.
- ^ Smith 1958, Vol. 1, Chapter VII.4.
- ^ Struik 1987, p. 96.
- ^ Boyer 1991, pp. 241–242.
- ^ Struik 1987, p. 97.
- ^ Boyer & 19991, pp. 241–242.
References
- Boyer, Carl B. (1991). "Greek Trigonometry and Mensuration, and The Arabic Hegemony". A History of Mathematics (2nd ed.). New York City: John Wiley & Sons. ISBN 0471543977.
{{cite book}}
: Invalid|ref=harv
(help) - Katz, Victor J. (1993). A History of Mathematics: An Introduction. HarperCollins college publishers. ISBN 0-673-38039-4.
{{cite book}}
: Invalid|ref=harv
(help). - Ronan, Colin A. (1983). The Cambridge Illustrated History of the World's Science. Cambridge University Press. ISBN 0521258448.
{{cite book}}
: Invalid|ref=harv
(help) - Smith, David E. (1958). History of Mathematics. Dover Publications. ISBN 0-486-20429-4.
{{cite book}}
: Invalid|ref=harv
(help) - Struik, Dirk J. (1987). A Concise History of Mathematics (4th rev. ed.). Dover Publications. ISBN 0486602559.
{{cite book}}
: Invalid|ref=harv
(help)
Further reading
- Books on Islamic mathematics
- Berggren, J. Lennart (1986), Episodes in the Mathematics of Medieval Islam, New York: Springer-Verlag, ISBN 0-387-96318-9
- Review: Toomer, Gerald J.; Berggren, J. L. (1988), "Episodes in the Mathematics of Medieval Islam", American Mathematical Monthly, 95 (6), Mathematical Association of America: 567, doi:10.2307/2322777, JSTOR 2322777
- Review: Hogendijk, Jan P.; Berggren, J. L. (1989), "Episodes in the Mathematics of Medieval Islam by J. Lennart Berggren", Journal of the American Oriental Society, 109 (4), American Oriental Society: 697–698, doi:10.2307/604119, JSTOR 604119)
- Daffa', Ali Abdullah al- (1977), The Muslim contribution to mathematics, London: Croom Helm, ISBN 0-85664-464-1
- Rashed, Roshdi (2001), The Development of Arabic Mathematics: Between Arithmetic and Algebra, Transl. by A. F. W. Armstrong, Springer, ISBN 0792325656
- Youschkevitch, Adolf P. (1960), Die Mathematik der Länder des Ostens im Mittelalter, Berlin
{{citation}}
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ignored (|author=
suggested) (help)CS1 maint: location missing publisher (link) Sowjetische Beiträge zur Geschichte der Naturwissenschaft pp. 62–160. - Youschkevitch, Adolf P. (1976), Les mathématiques arabes: VIIIe-XVe siècles, translated by M. Cazenave and K. Jaouiche, Paris: Vrin, ISBN 978-2-7116-0734-1
- Book chapters on Islamic mathematics
- Berggren, J. Lennart (2007), "Mathematics in Medieval Islam", in Victor J. Katz (ed.), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (Second ed.), Princeton, New Jersey: Princeton University, ISBN 9780691114859
{{citation}}
: CS1 maint: ref duplicates default (link) - Cooke, Roger (1997), "Islamic Mathematics", The History of Mathematics: A Brief Course, Wiley-Interscience, ISBN 0471180823
- Books on Islamic science
- Daffa, Ali Abdullah al-; Stroyls, J.J. (1984), Studies in the exact sciences in medieval Islam, New York: Wiley, ISBN 0471903205
- Kennedy, E. S. (1984), Studies in the Islamic Exact Sciences, Syracuse Univ Press, ISBN 0815660677
- Books on the history of mathematics
- Joseph, George Gheverghese (2000), The Crest of the Peacock: Non-European Roots of Mathematics (2nd ed.), Princeton University Press, ISBN 0691006598 (Reviewed: Katz, Victor J.; Joseph, George Gheverghese (1992), "The Crest of the Peacock: Non-European Roots of Mathematics by George Gheverghese Joseph", The College Mathematics Journal, 23 (1), Mathematical Association of America: 82–84, doi:10.2307/2686206, JSTOR 2686206)
- Youschkevitch, Adolf P. (1964), Gesichte der Mathematik im Mittelalter, Leipzig: BG Teubner Verlagsgesellschaft
- 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.
- Sánchez Pérez, José A. (1921), Biografías de Matemáticos Árabes que florecieron en España, Madrid: Estanislao Maestre
- Sezgin, Fuat (1997), Geschichte Des Arabischen Schrifttums (in German), Brill Academic Publishers, ISBN 9004020071
- Suter, Heinrich (1900), Die Mathematiker und Astronomen der Araber und ihre Werke, Abhandlungen zur Geschichte der Mathematischen Wissenschaften Mit Einschluss Ihrer Anwendungen, X Heft, Leipzig
{{citation}}
: CS1 maint: location missing publisher (link)
- Television documentaries
- Marcus du Sautoy (presenter) (2008). "The Genius of the East". The Story of Maths. BBC.
- Jim Al-Khalili (presenter) (2010). Science and Islam. BBC.
External links
- Hogendijk, Jan P. (January 1999). "Bibliography of Mathematics in Medieval Islamic Civilization".
{{cite web}}
: Invalid|ref=harv
(help)CS1 maint: date and year (link) - O'Connor, John J.; Robertson, Edmund F. (1999), "Arabic mathematics: forgotten brilliance?", MacTutor History of Mathematics Archive, University of St Andrews