Jamjid Masʿud al-Kashi

Ghiyath ad-Din Jamschid bin Masʿud bin Muhammad al-Kaschi ( Arabic غياث الدين جمشید بن مسعود بن محمد الكاشي, DMG Ġiyāṯ ad-Dīn Ǧamšīd bin Masʿūd bin Muḥammad al-Kāšī ; Persian غیاث‌الدین جمشید کاشانی Ghiyāth-ad-Dīn Ǧamšīd Kāšānī ; * around 1380 in Kashan , Iran ; † June 22, 1429 in Samarkand , Timurid Empire , today in Uzbekistan ) was a Persian doctor, mathematician and astronomer of the High Middle Ages.

In France, the cosine theorem is called Théorème d'Al-Kashi .

life and work

At a young age he had to earn his living as a doctor and could only study mathematics and astronomy on the side. Despite all adversities, he compiled a new catalog of stars based on the Zij-i Ilchani (table of the Ilchans ) of at-Tusi , which also contained a collection of mathematical equations for astronomy such as formulas for the transformation of ecliptical to equatorial coordinates and tables of trigonometric functions . It is known as Chagani Zij , tablets of the khan , as he dedicated it to either the Timurid prince Shāh Ruch or his son Ulug Beg . Ulug Beg recognized the extraordinary abilities of al-Kashi and in 1420 appointed him to his newly founded Madresse in Samarkand . He was the most important advisor in the design and construction of the Gurkani Zidsch observatory attached to the Madresse .

Long unsurpassed results were achieved by numerical solutions. In the ar-Risala al-Muhitiya ( lesson on the circumference of a circle), for example, he determined the circumference of the unit circle ( i.e. double the number of circles ) from the 3 * 2 ²⁸ corner to 9 sexagesimal places : 6; 16,59,28,01,34 , 51,46,14,50 , which he converted into the Indian digits 6,2831853071795865 with 16 correct decimal places. This is one of the oldest documents on calculating with decimal fractions. With this he improved the result of the Chinese mathematician Zu Chongzhi , who had calculated to 7 digits. al-Kaschi was not surpassed until 1596 by Ludolph van Ceulen , who after 30 years of work had calculated 35 decimal places. ${\displaystyle \pi }$ ${\displaystyle \pi }$

Whether he or Ulug Beg calculated the sine of 1 ° with high accuracy is disputed among historians (see Ulugbek Madrasa ). It is noteworthy that Qadi Zada , his colleague at the madrasah , achieved the same result in a different way. He advocated the replacement of fractions in the sexagesimal system with decimal fractions. To make it easier to predict planetary locations , he built a kind of analog computer , the Tabaq al-Manateq , which was constructed like an astrolabe . The input was information from planet tables that were contained in astronomy books such as his Chagani Zij. This device corresponds to the Volvellen that were often included in late medieval European astronomy books.

He wrote the five-volume textbook Miftah al-Hisab , which was widely used in the Muslim world for a long time, to train the students of the Madresse in mathematics and for applications in astronomy, land surveying and architecture . At the time of his death, astronomical observations at the observatory had only just begun. His successor as leader was Qadi Zada . The summary of the work, the Zij-i-Sultani , was based on al- Kaschi's Chagani Zij .

Letters that al-Kashi wrote to his father in Kashan are one of the most important sources for life at court and in the Madresse in Samarkand.

Manuscript from the Central Library of Astan Quds Razavi

Works

• Khagani Zij . (The Khan's Astronomical Tables) 1413
• ar-Risala al-Muhitiya. (The lesson on the circumference) 1424.
• Miftah al-Hisab. (Key of Calculation) 1427.

literature

• ES Kennedy: A Fifteenth-Century Planetary Computer: al-Kāshī's “Ṭabaq al-Manāṭeq”. I. Motion of the Sun and Moon in Longitude. In: Isis . 1950, Volume 41 (124: 2), pages 180-183.
• Paul Luckey: The art of arithmetic at Gamsid b. Mas'ud a-Kasi . Treatises for the customer of the Orient XXXI, 1. Wiesbaden 1951.
• Paul Luckey: The lesson on the circumference of Gamsid b. Mas'ud al-Kasi . Treatises of the German Academy of Sciences in Berlin, Class for Mathematics, born 1950, No. 6. Berlin 1953.
• Javad Hamadanizadeh: The trigonometric Tables of al-Kashi in his Zij-i Khaqani. Historia mathematica, 7: 38-45 (1980).

Web links

Commons : Jamjid Masʿud al-Kashi  - Collection of images, videos and audio files

• Literature by and about Jamschid Masʿud al-Kaschi in the catalog of the German National Library
• Biographies of Al-Kashi and Quadi Zada
• John J. O'Connor, Edmund F. Robertson :  Jamschid Masʿud al-Kaschi. In: MacTutor History of Mathematics archive .