KamÃÂl al-Dën ibn Yà «nus (1156âÂÂ1242) 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.
A biography of Ibn Yà «nus appears in the of Ibn Abë Uá¹£aybiÿa. An even longer one is found in the of Ibn KhallikÃÂn, whose father was a friend of Ibn Yà «nus. Ibn Abë Uá¹£aybiÿa gives his as Abà « ÿImrÃÂn, while Ibn KhallikÃÂn gives it as Abà « al-Fatḥ. KamÃÂl al-Dën was his , while his given name was Mà «sàand his (patronymic) was ibn Yà «nus ibn Muḥammad ibn Manÿat.
Ibn Yà «nus was born in Mosul in 1156 (AH 551) and studied in Baghdad. He became expert in astronomy, mathematics, medicine, theology and Greek philosophy or . In Islamic law, he belonged to the ShÃÂfiÿë school. He also had a reputation for philology.
Ibn Yà «nus returned to Mosul to teach, setting up a school in a local mosque. He became "the most learned and sought-after teacher in the Islamic world of his generation" and "one of the main attractions of Mosul". In the words of Ibn Abë Uá¹£aybiÿa, he was "the paragon of the scholars and the chief of the philosophers". He taught the interpretation of the Qurþan, the Torah and the Gospels, even attracting Christian and Jewish student. According to Bar Hebraeus, the Antiochene Christian scholar Theodore of Antioch studied al-FÃÂrÃÂbë, Ibn SënÃÂ, Euclid and Ptolemy under Ibn Yà «nus in Mosul and later returned there for further study. Among his other students were Naṣër al-Dën al-á¹¬à «së, SirÃÂj al-Din Urmawë, ÿAlam al-Dën Qayá¹£ar and Athër al-Dën al-Abharë.
During negotiations to end the Sixth Crusade in 1229, the Emperor Frederick II sent a set of mathematical questions to Sultan al-KÃÂmil asking for solutions. According to al-Qazwënë, the sultan passed them along to Ibn Yà «nus, although Ibn Abë Uá¹£aybiÿa records that an imperial envoy was dispatched to the atabeg of Mosul, Badr al-Dën Luþluþ, who sent him on to the scholar. Ibn Abë Uá¹£aybiÿa uses the story to demonstrate Ibn Yà «nus's knowledge of "magic" (). Since "Ibn Yà «nus 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 Yà «nus died in Mosul in 1242 (AH 639).
Only Ibn Yà «nus's mathematical works survive. Four are known:
In response to a query from Frederick II, Ibn Yà «nus gave a method for determining the quadrature of a circular segment. Another problem addressed by Ibn Yà «nus was later used by his former student, Theodore of Antioch, to test Leonardo Fibonacci. The problem asks, for what integer values of x, y and z is each of the following sums the square of an integer:
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-á¹¬à «së.