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	'''{{transl\|ar\|ALA\|Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ}}''' (Abu Kamil, {{lang-ar\|ابو كامل}}, also called ''al-Ḥasib al-Miṣrī''—literally, "the Egyptian calculator") (c. 850 – c. 930) was an ] ] during the ]. Abu Kamil made important contributions to the field of ]~~, and was the first to recognize ] as its "inventor"~~.<ref name=MacTutor>{{MacTutor Biography\|id=Abu_Kamil}}</ref> His mathematical techniques were later adopted by ]~~, thus allowing Abu Kamil an important part in introducing algebra to Europe~~.<ref name=MacTutor /> Other European mathematicians learned about the ] through translations of his books.<ref name="Livio">{{cite book \| last = Livio \| first = Mario \| title = The Golden Ratio \| publisher = Broadway \| location = New York \| year = 2003 \| isbn = 0-7679-0816-3 \| pages=89-90,92,96}}</ref~~> He may also have been the first mathematician "who instead of simply finding a solution to a problem was interested in finding ''all'' the possible solutions".<ref name="Livio" /~~>		'''{{transl\|ar\|ALA\|Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ}}''' (Abu Kamil, {{lang-ar\|ابو كامل}}, also called ''al-Ḥasib al-Miṣrī''—literally, "the Egyptian calculator") (c. 850 – c. 930) was an ] ] during the ]. Abu Kamil made important contributions to the field of ].<ref name=MacTutor>{{MacTutor Biography\|id=Abu_Kamil}}</ref> His mathematical techniques were later adopted by ].<ref name=MacTutor /> Other European mathematicians learned about the ] through translations of his books.<ref name="Livio">{{cite book \| last = Livio \| first = Mario \| title = The Golden Ratio \| publisher = Broadway \| location = New York \| year = 2003 \| isbn = 0-7679-0816-3 \| pages=89-90,92,96}}</ref>

	==Works==		==Works==

	Abu Kamil's major work is ''The Book of Rare Things in the Art of Calculation'' (Kitāb al-ṭarā’if fi’l-ḥisāb), ~~which~~ describes a number of systematic procedures for finding ] for ]. Such procedures were not known to many of his peers. This work led to further research into ] and solutions of ] by ~~other~~ ~~notable scientists, like~~ ] and ], ~~which~~ had a lasting impact on the development of algebra.<ref name="Levey2008">{{cite encyclopedia \| last = Levey \| first = Martin \| title = \| encyclopedia = ] \| publisher = Encyclopedia.com \| origyear=1970-80 \| year = 2008 }}</ref> In this book he describes one problem for which he found 2,678 solutions.<ref name="Livio" />		Abu Kamil's major work, ''The Book of Rare Things in the Art of Calculation'' (Kitāb al-ṭarā’if fi’l-ḥisāb), describes a number of systematic procedures for finding ] for ]. Such procedures were not known to many of his peers. This work led to further research into ] and solutions of ] by mathematicians including ] and ], and as such had a lasting impact on the development of algebra.<ref name="Levey2008">{{cite encyclopedia \| last = Levey \| first = Martin \| title = \| encyclopedia = ] \| publisher = Encyclopedia.com \| origyear=1970-80 \| year = 2008 }}</ref> In this book he describes one problem for which he found 2,678 solutions.<ref name="Livio" />

	His other major work is ''On the Pentagon and Decagon'' (Kitāb … al-mukhammas wa’al-mu‘ashshar), where he solved systems of ]s whose solutions are ] and ], and accepted irrational numbers (often in the form of a ], ] or ]) as solutions and ]s to ]s.<ref name="Sesiano">Jacques Sesiano, "Islamic mathematics", p. 148, in {{Cite book\|title=Mathematics Across Cultures: The History of Non-Western Mathematics\|first1=Helaine\|last1=Selin\|first2=Ubiratan\|last2=D'Ambrosio\|year=2000\|publisher=]\|isbn=1-4020-0260-2}}</ref> Abu Kamil is considered the first to systematically use and accept ]s as ]ic objects.<ref name="Sesiano" /> Some of his calculations in this book used the ].<ref name="Livio" />		His other major work is ''On the Pentagon and Decagon'' (Kitāb … al-mukhammas wa’al-mu‘ashshar), where he solved systems of ]s whose solutions are ] and ], and accepted irrational numbers (often in the form of a ], ] or ]) as solutions and ]s to ]s.<ref name="Sesiano">Jacques Sesiano, "Islamic mathematics", p. 148, in {{Cite book\|title=Mathematics Across Cultures: The History of Non-Western Mathematics\|first1=Helaine\|last1=Selin\|first2=Ubiratan\|last2=D'Ambrosio\|year=2000\|publisher=]\|isbn=1-4020-0260-2}}</ref> Abu Kamil is considered the first to systematically use and accept ]s as ]ic objects.<ref name="Sesiano" /> Some of his calculations in this book used the ].<ref name="Livio" />

Revision as of 19:42, 14 March 2011

Abū Kāmil Shujā ibn Aslam
Born	c. 850
Died	c. 930

Academic work
Era	Islamic Golden Age
Main interests	Algebra, Geometry
Notable works	The Book of Rare Things in the Art of Calculation
Influenced	Fibonacci

Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ (Abu Kamil, Template:Lang-ar, also called al-Ḥasib al-Miṣrī—literally, "the Egyptian calculator") (c. 850 – c. 930) was an Egyptian Muslim mathematician during the Islamic Golden Age. Abu Kamil made important contributions to the field of algebra. His mathematical techniques were later adopted by Fibonacci. Other European mathematicians learned about the Hindu-Arabic numerals through translations of his books.

Works

Abu Kamil's major work, The Book of Rare Things in the Art of Calculation (Kitāb al-ṭarā’if fi’l-ḥisāb), describes a number of systematic procedures for finding integral solutions for indeterminate equations. Such procedures were not known to many of his peers. This work led to further research into real numbers and solutions of polynomials by mathematicians including al-Karaji and al-Samawʾal, and as such had a lasting impact on the development of algebra. In this book he describes one problem for which he found 2,678 solutions.

His other major work is On the Pentagon and Decagon (Kitāb … al-mukhammas wa’al-mu‘ashshar), where he solved systems of equations whose solutions are whole numbers and fractions, and accepted irrational numbers (often in the form of a square root, cube root or fourth root) as solutions and coefficients to quadratic equations. Abu Kamil is considered the first to systematically use and accept irrational numbers as algebraic objects. Some of his calculations in this book used the Golden Ratio.

He also wrote Kitāb al-Misāḥa, a manual of geometry for non-mathematicians, like land surveyors and other government officials.

Ḥajjī Khalīfa attributed to him a book on algebraic solutions for problems related to Islamic inheritance.

Another achievement of Abu Kamil is solving three non-linear simultaneous equations with three unknown variables. He is also considered as the first Islamic mathematician to work with algebraic equations with powers higher than $x^{2}$ . In some of his books he wrote all the mathematical problems rhetorically, lacking any mathematical notation beside the numbers. For example, he uses the expression "square square root" for $x^{5}$ (i.e. $x^{2}$ · $x^{2}$ · $x$ ).

Many of Abu Kamil's examples and algebraic techniques were later copied by Fibonacci in his Practica geometriae and other works.

Notes

^ O'Connor, John J.; Robertson, Edmund F., "Abu Kamil", MacTutor History of Mathematics Archive, University of St Andrews
^ Livio, Mario (2003). The Golden Ratio. New York: Broadway. pp. 89–90, 92, 96. ISBN 0-7679-0816-3.
^ Levey, Martin (2008) . "Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad ibn Shujā". Complete Dictionary of Scientific Biography. Encyclopedia.com. {{cite encyclopedia}}: External link in |title= (help)
^ Jacques Sesiano, "Islamic mathematics", p. 148, in Selin, Helaine; D'Ambrosio, Ubiratan (2000). Mathematics Across Cultures: The History of Non-Western Mathematics. Springer. ISBN 1-4020-0260-2.
Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. p. 518. ISBN 978-0-691-11485-9.

External links

Levey, Martin (2008) . "Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad ibn Shujā". Complete Dictionary of Scientific Biography. Encyclopedia.com. {{cite encyclopedia}}: External link in |title= (help)
O'Connor, John J.; Robertson, Edmund F., "Abu Kamil", MacTutor History of Mathematics Archive, University of St Andrews

Mathematics in the medieval Islamic world

Mathematicians

9th century	'Abd al-Hamīd ibn Turk Sanad ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Qusta ibn Luqa Al-Mahani al-Dinawari Banū Mūsā brothers Hunayn ibn Ishaq Al-Khwarizmi Yusuf al-Khuri Ishaq ibn Hunayn Na'im ibn Musa Thābit ibn Qurra al-Marwazi Abu Said Gorgani
10th century	Abu al-Wafa al-Khazin Al-Qabisi Abu Kamil Ahmad ibn Yusuf Aṣ-Ṣaidanānī Sinān ibn al-Fatḥ al-Khojandi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus al-Uqlidisi Al-Battani Sinan ibn Thabit Ibrahim ibn Sinan Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud Al-Sijzi Al-Karaji al-Majriti al-Jabali
11th century	Abu Nasr Mansur Alhazen Kushyar Gilani Al-Biruni Ibn al-Samh Abu Mansur al-Baghdadi Avicenna al-Jayyānī al-Nasawī al-Zarqālī ibn Hud Al-Isfizari Omar Khayyam Muhammad al-Baghdadi
12th century	Jabir ibn Aflah Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi al-Hassar Sharaf al-Din al-Tusi Ibn al-Yasamin
13th century	Ibn al‐Ha'im al‐Ishbili Ahmad al-Buni Ibn Munim Alam al-Din al-Hanafi Ibn Adlan al-Urdi Nasir al-Din al-Tusi al-Abhari Muhyi al-Din al-Maghribi al-Hasan al-Marrakushi Qutb al-Din al-Shirazi Shams al-Din al-Samarqandi Ibn al-Banna' Kamāl al-Dīn al-Fārisī
14th century	Nizam al-Din al-Nisapuri Ibn al-Shatir Ibn al-Durayhim Al-Khalili al-Umawi
15th century	Ibn al-Majdi al-Rūmī al-Kāshī Ulugh Beg Ali Qushji al-Wafa'i al-Qalaṣādī Sibt al-Maridini Ibn Ghazi al-Miknasi
16th century	Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi

Mathematical
works

Concepts

Centers

Influences

Influenced

Template:Persondata

Categories:

Revision as of 05:12, 25 February 2011 editAl-Andalusi (talk \| contribs)Extended confirmed users12,094 edits Added Infobox scholar← Previous edit		Revision as of 19:42, 14 March 2011 edit undoDialectric (talk \| contribs)Extended confirmed users, Rollbackers41,670 edits partial rewording and condensing for neutralityNext edit →
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	}}		}}

	'''{{transl\|ar\|ALA\|Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ}}''' (Abu Kamil, {{lang-ar\|ابو كامل}}, also called ''al-Ḥasib al-Miṣrī''—literally, "the Egyptian calculator") (c. 850 – c. 930) was an ] ] during the ]. Abu Kamil made important contributions to the field of ]~~, and was the first to recognize ] as its "inventor"~~.<ref name=MacTutor>{{MacTutor Biography\|id=Abu_Kamil}}</ref> His mathematical techniques were later adopted by ]~~, thus allowing Abu Kamil an important part in introducing algebra to Europe~~.<ref name=MacTutor /> Other European mathematicians learned about the ] through translations of his books.<ref name="Livio">{{cite book \| last = Livio \| first = Mario \| title = The Golden Ratio \| publisher = Broadway \| location = New York \| year = 2003 \| isbn = 0-7679-0816-3 \| pages=89-90,92,96}}</ref~~> He may also have been the first mathematician "who instead of simply finding a solution to a problem was interested in finding ''all'' the possible solutions".<ref name="Livio" /~~>		'''{{transl\|ar\|ALA\|Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ}}''' (Abu Kamil, {{lang-ar\|ابو كامل}}, also called ''al-Ḥasib al-Miṣrī''—literally, "the Egyptian calculator") (c. 850 – c. 930) was an ] ] during the ]. Abu Kamil made important contributions to the field of ].<ref name=MacTutor>{{MacTutor Biography\|id=Abu_Kamil}}</ref> His mathematical techniques were later adopted by ].<ref name=MacTutor /> Other European mathematicians learned about the ] through translations of his books.<ref name="Livio">{{cite book \| last = Livio \| first = Mario \| title = The Golden Ratio \| publisher = Broadway \| location = New York \| year = 2003 \| isbn = 0-7679-0816-3 \| pages=89-90,92,96}}</ref>

	==Works==		==Works==

	Abu Kamil's major work is ''The Book of Rare Things in the Art of Calculation'' (Kitāb al-ṭarā’if fi’l-ḥisāb), ~~which~~ describes a number of systematic procedures for finding ] for ]. Such procedures were not known to many of his peers. This work led to further research into ] and solutions of ] by ~~other~~ ~~notable scientists, like~~ ] and ], ~~which~~ had a lasting impact on the development of algebra.<ref name="Levey2008">{{cite encyclopedia \| last = Levey \| first = Martin \| title = \| encyclopedia = ] \| publisher = Encyclopedia.com \| origyear=1970-80 \| year = 2008 }}</ref> In this book he describes one problem for which he found 2,678 solutions.<ref name="Livio" />		Abu Kamil's major work, ''The Book of Rare Things in the Art of Calculation'' (Kitāb al-ṭarā’if fi’l-ḥisāb), describes a number of systematic procedures for finding ] for ]. Such procedures were not known to many of his peers. This work led to further research into ] and solutions of ] by mathematicians including ] and ], and as such had a lasting impact on the development of algebra.<ref name="Levey2008">{{cite encyclopedia \| last = Levey \| first = Martin \| title = \| encyclopedia = ] \| publisher = Encyclopedia.com \| origyear=1970-80 \| year = 2008 }}</ref> In this book he describes one problem for which he found 2,678 solutions.<ref name="Livio" />

	His other major work is ''On the Pentagon and Decagon'' (Kitāb … al-mukhammas wa’al-mu‘ashshar), where he solved systems of ]s whose solutions are ] and ], and accepted irrational numbers (often in the form of a ], ] or ]) as solutions and ]s to ]s.<ref name="Sesiano">Jacques Sesiano, "Islamic mathematics", p. 148, in {{Cite book\|title=Mathematics Across Cultures: The History of Non-Western Mathematics\|first1=Helaine\|last1=Selin\|first2=Ubiratan\|last2=D'Ambrosio\|year=2000\|publisher=]\|isbn=1-4020-0260-2}}</ref> Abu Kamil is considered the first to systematically use and accept ]s as ]ic objects.<ref name="Sesiano" /> Some of his calculations in this book used the ].<ref name="Livio" />		His other major work is ''On the Pentagon and Decagon'' (Kitāb … al-mukhammas wa’al-mu‘ashshar), where he solved systems of ]s whose solutions are ] and ], and accepted irrational numbers (often in the form of a ], ] or ]) as solutions and ]s to ]s.<ref name="Sesiano">Jacques Sesiano, "Islamic mathematics", p. 148, in {{Cite book\|title=Mathematics Across Cultures: The History of Non-Western Mathematics\|first1=Helaine\|last1=Selin\|first2=Ubiratan\|last2=D'Ambrosio\|year=2000\|publisher=]\|isbn=1-4020-0260-2}}</ref> Abu Kamil is considered the first to systematically use and accept ]s as ]ic objects.<ref name="Sesiano" /> Some of his calculations in this book used the ].<ref name="Livio" />

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