Kamal al-Din ibn Yunus

Template:Short description Kamāl al-Dīn ibn Yūnus (1156–1242) was an Iraqi Muslim polymath known for his writings on mathematics, although he also studied and taught astronomy, theology, philology, law, philosophy and medicine. For many years he taught Muslim, Christian and Jewish pupils at his own school in his native city of Mosul.

Life

A biography of Ibn Yūnus appears in the Template:Lang of Ibn Abī Uṣaybiʿa. An even longer one is found in the Template:Lang of Ibn Khallikān, whose father was a friend of Ibn Yūnus.Template:Sfn Ibn Abī Uṣaybiʿa gives his Template:Lang as Abū ʿImrān, while Ibn Khallikān gives it as Abū al-Fatḥ. Kamāl al-Dīn was his Template:Lang, while his given name was Mūsā and his Template:Lang (patronymic) was ibn Yūnus ibn Muḥammad ibn Manʿat.

Ibn Yūnus was born in Mosul in 1156 (AH 551) and studied in Baghdad.Template:SfnTemplate:Sfn He became expert in astronomy, mathematics, medicine, theology and Greek philosophy or Template:Lang.Template:SfnTemplate:SfnTemplate:Sfn In Islamic law, he belonged to the Shāfiʿī school.Template:SfnTemplate:Sfn He also had a reputation for philology.Template:Sfn

Ibn Yūnus returned to Mosul to teach, setting up a school in a local mosque.Template:SfnTemplate:Sfn He became "the most learned and sought-after teacher in the Islamic world of his generation"Template:Sfn and "one of the main attractions of Mosul".Template:Sfn In the words of Ibn Abī Uṣaybiʿa, he was "the paragon of the scholars and the chief of the philosophers". He taught the interpretation of the Qurʾan, the Torah and the Gospels, even attracting Christian and Jewish student.Template:Sfn According to Bar Hebraeus, the Antiochene Christian scholar Theodore of Antioch studied al-Fārābī, Ibn Sīnā, Euclid and Ptolemy under Ibn Yūnus in Mosul and later returned there for further study.Template:Sfn Among his other students were Naṣīr al-Dīn al-Ṭūsī,Template:SfnTemplate:Sfn Sirāj al-Din Urmawī,Template:Sfn ʿAlam al-Dīn QayṣarTemplate:Sfn and Athīr al-Dīn al-Abharī.Template:Sfn

During negotiations to end the Sixth Crusade in 1229, the Emperor Frederick II sent a set of mathematical questions to Sultan al-Kāmil asking for solutions. According to al-Qazwīnī, the sultan passed them along to Ibn Yūnus, although Ibn Abī Uṣaybiʿa records that an imperial envoy was dispatched to the atabeg of Mosul, Badr al-Dīn Luʾluʾ, who sent him on to the scholar.Template:Sfn Ibn Abī Uṣaybiʿa uses the story to demonstrate Ibn Yūnus's knowledge of "magic" (Template:Lang). Since "Ibn Yūnus used to wear rough clothes without affectation and had no knowledge of the things of the world", the atabeg demanded that the scholar "prepare a splendid salon" for the envoy. The scholar's students then found his room "adorned with the most beautiful and finest Byzantine carpets with a group of slaves and servants in fine clothes", but as soon as "the emissary had gone all that we had seen before vanished".

Ibn Yūnus died in Mosul in 1242 (AH 639).Template:SfnTemplate:Sfn

Works

Only Ibn Yūnus's mathematical works survive.Template:SfnTemplate:Sfn Four are known:

• Treatise on Proof of the Premise Neglected by Archimedes in His Book on the Division of a Cirlce to Seven Parts and on the Property of Its UseTemplate:Sfn
• Commentary on Geometric ConstructionTemplate:Sfn
• Treatise on Proof that it is Impossible for Two Odd Square Numbers to Exist so that Their Sum is SquareTemplate:Sfn
• Treatise on Proof of two Premises Neglected by Apollonius at the End of the First Book of Conic SectionsTemplate:Sfn

In response to a query from Frederick II, Ibn Yūnus gave a method for determining the quadrature of a circular segment.Template:Sfn Another problem addressed by Ibn Yūnus was later used by his former student, Theodore of Antioch, to test Leonardo Fibonacci.Template:Sfn The problem asks, for what integer values of x, y and z is each of the following sums the square of an integer:Template:Sfn

$x+y+z+x^2$

$x+y+z+x^2+y^2$

$x+y+z+x^2+y^2+z^2$

In addition to his mathematical treatises, Khayr al-Din al-Zirikli in his Alam describes a Book on Sultan's Mysteries on Stars and Paul Kunitsche reported seeing a manuscript of a treatise on the linear astrolabe, the Treatise on the Stick of Sharaf al-Ṭūsī.Template:Sfn

Bibliography

• Template:Cite thesis
• Template:Cite book [Originally published in Federico II e le Nuove Culture: Atti del XXXI Convegno Storico Internazionale, Todi, 9–12 ottobre, 1994 (Spoleto: 1995).]
• Template:Cite book
• Template:Cite book
• Template:Cite book
• Template:Cite book
• Template:Cite book