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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, and was the first to recognize Al-Khwarizmi as its "inventor". His mathematical techniques were later adopted by Fibonacci, thus allowing Abu Kamil an important part in introducing algebra to Europe. Other European mathematicians learned about the Hindu-Arabic numerals through translations of his books. 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".

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 ${\displaystyle x^{2}}$. 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 ${\displaystyle x^{5}}$ (i.e. ${\displaystyle x^{2}}$ · ${\displaystyle x^{2}}$ · ${\displaystyle x}$).

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

Notes

1. ^ O'Connor, John J.; Robertson, Edmund F., "Abu Kamil", MacTutor History of Mathematics Archive, University of St Andrews
2. ^ Livio, Mario (2003). The Golden Ratio. New York: Broadway. pp. 89–90, 92, 96. ISBN 0-7679-0816-3.
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)
4. ^ 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.
5. 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.

Further reading

• Levey, Martin (1970). "Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad ibn Shujā". Dictionary of Scientific Biography. Vol. 1. New York: Charles Scribner's Sons. pp. 30–32. ISBN 0684101149.
• Djebbar, Ahmed. Une histoire de la science arabe: Entretiens avec Jean Rosmorduc. Seuil (2001)

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

v t e 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	The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Book on the Measurement of Plane and Spherical Figures Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij
Concepts	Alhazen's problem Islamic geometric patterns
Centers	Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi ad-Din Madrasa Maragheh observatory University of al-Qarawiyyin
Influences	Babylonian mathematics Greek mathematics Indian mathematics
Influenced	Byzantine mathematics European mathematics Indian mathematics
Related	Hindu–Arabic numeral system Arabic numerals (Eastern Arabic numerals, Western Arabic numerals) Trigonometric functions History of trigonometry History of algebra

Template:Persondata

• Islamic mathematics
• Arab mathematicians
• Egyptian mathematicians
• 9th-century mathematicians
• 10th-century mathematicians
• Algebraists
• 850 births
• 930 deaths
• Egyptian Muslims