Abu Kamil

Abu Kamil
أبو كامل
Abu Kamil ; أبو كامل
Born	c. 850
Died	c. 930
Other names	Al-ḥāsib al-miṣrī
Academic background
Influences	Al-Khwarizmi
Academic work
Era	Islamic Golden Age ; (Middle Abbasid era)
Main interests	Algebra, geometry
Notable works	The Book of Algebra
Notable ideas	Use of irrational numbers as solutions and coefficients to equations;
Influenced	Al-Karaji, Fibonacci

Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ (Latinized as Auoquamel,^[1] Arabic: أبو كامل شجاع بن أسلم بن محمد بن شجاع, also known as Al-ḥāsib al-miṣrī—lit. "The Egyptian Calculator") (c. 850 – c. 930) was a prominent Egyptian mathematician during the Islamic Golden Age. He is considered the first mathematician to systematically use and accept irrational numbers as solutions and coefficients to equations.^[2] His mathematical techniques were later adopted by Fibonacci, thus allowing Abu Kamil an important part in introducing algebra to Europe.^[3]

Abu Kamil made important contributions to algebra and geometry.^[4] He was the first Islamic mathematician to work easily with algebraic equations with powers higher than $x^{2}$ (up to $x^{8}$ ),^[3]^[5] and solved sets of non-linear simultaneous equations with three unknown variables.^[6] He illustrated the rules of signs for expanding the multiplication $(a\pm b)(c\pm d)$ .^[7] He wrote all problems rhetorically, and some of his books lacked any mathematical notation beside those of integers. For example, he uses the Arabic expression "māl māl shayʾ" ("square-square-thing") for $x^{5}$ (as $x^{5}=x^{2}\cdot x^{2}\cdot x$ ).^[3]^[8] One notable feature of his works was enumerating all the possible solutions to a given equation.^[9]

The Muslim encyclopedist Ibn Khaldūn classified Abū Kāmil as the second greatest algebraist chronologically after al-Khwarizmi.^[10]

^ Rāshid, Rushdī; Régis Morelon (1996). Encyclopedia of the history of Arabic science. Vol. 2. Routledge. p. 240. ISBN 978-0-415-12411-9.
^ Cite error: The named reference Sesiano was invoked but never defined (see the help page).
^ ^a ^b ^c Cite error: The named reference MacTutor was invoked but never defined (see the help page).
^ Cite error: The named reference EI2 was invoked but never defined (see the help page).
^ Cite error: The named reference Levey2008 was invoked but never defined (see the help page).
^ Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. pp. 518, 550. ISBN 978-0-691-11485-9.
^ Mat Rofa Bin Ismail (2008), "Algebra in Islamic Mathematics", in Helaine Selin (ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, vol. 1 (2nd ed.), Springer, p. 114, ISBN 9781402045592
^ Bashmakova, Izabella Grigorʹevna; Galina S. Smirnova (2000-01-15). The beginnings and evolution of algebra. Cambridge University Press. p. 52. ISBN 978-0-88385-329-0.
^ Cite error: The named reference HSTM was invoked but never defined (see the help page).
^ Sesiano, Jacques (2008). "Abū Kāmil". Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer Netherlands: 7–8. doi:10.1007/978-1-4020-4425-0_9198. ISBN 978-1-4020-4559-2.

[1] Rāshid, Rushdī; Régis Morelon (1996). Encyclopedia of the history of Arabic science. Vol. 2. Routledge. p. 240. ISBN 978-0-415-12411-9.

[Sesiano-2] Cite error: The named reference Sesiano was invoked but never defined (see the help page).

[MacTutor-3] Cite error: The named reference MacTutor was invoked but never defined (see the help page).

[EI2-4] Cite error: The named reference EI2 was invoked but never defined (see the help page).

[Levey2008-5] Cite error: The named reference Levey2008 was invoked but never defined (see the help page).

[Berggren-6] Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. pp. 518, 550. ISBN 978-0-691-11485-9.

[Ismail-7] Mat Rofa Bin Ismail (2008), "Algebra in Islamic Mathematics", in Helaine Selin (ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, vol. 1 (2nd ed.), Springer, p. 114, ISBN 9781402045592

[8] Bashmakova, Izabella Grigorʹevna; Galina S. Smirnova (2000-01-15). The beginnings and evolution of algebra. Cambridge University Press. p. 52. ISBN 978-0-88385-329-0.

[HSTM-9] Cite error: The named reference HSTM was invoked but never defined (see the help page).

[10] Sesiano, Jacques (2008). "Abū Kāmil". Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer Netherlands: 7–8. doi:10.1007/978-1-4020-4425-0_9198. ISBN 978-1-4020-4559-2.

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Abu Kamil

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