Hellenica World


Shams al-Dīn Abū ʿAbd Allāh Muḥammad ibn Muḥammad al-Khalīlī (1320–1380) was an astronomer of Syria who compiled extensive tables for astronomical use.

Shams al-Din Abu Abdullah Muhammad ibn Muhammad al-Khalili worked in Damascus, Syria at the Umayyad Mosque as a religious timekeeper (muwaqqit) for the majority of his life. Other than al-Khalili’s occupation, little is known about his life. He lived at the same time as Ibn al-Shatir, the famous Arab astronomer.[1]

Al-Khalili is known for two sets of mathematical tables he constructed, both totaling roughly 30,000 entries. He tabulated all the entries made by the celebrated Egyptian Muslim astronomer Ibn Yunus, except for the entries that al-Khalili made himself for the city of Damascus. It is evident that number manipulation did not exhaust al-Khalili as he computed 13,000 entries into his ‘Universal Tables’ of different auxiliary functions which allowed him to generate the solutions of standard problems of spherical astronomy for any given latitude. In addition to this, he created a 3,000 entry table that gave the direction of the city of Mecca (the Qibla) for all latitudes and longitudes for all the Muslim countries of the 14th century.[2] Knowledge of the direction of the Qibla is essential in Islam because Muslims pray in the direction of Mecca. The values present in al-Khalili’s tables have been determined to be amazingly accurate – indeed they have been calculated to be accurate up to three or four significant decimal digits. Up to the present time, it is not known how exactly al-Khalili went about calculating each of his entries.[3]


^ D A King, Al-Khalili's qibla table, J. Near-Eastern Stud. 34 (2) (1975), 81-122. http://www.jstor.org/sici?sici=0022-2968(197504)34%3A2%3C81%3AAQT%3E2.0.CO%3B2-6
^ D A King, Al-Khalili's auxiliary tables for solving problems of spherical astronomy, J. Hist. Astronom. 4 (2) (1973), 99-110. http://adsabs.harvard.edu/full/1973JHA.....4...99K
^ G Van Brummelen, The numerical structure of al-Khalili's auxiliary tables, Physis Riv. Internaz. Storia Sci. (N.S.) 28 (3) (1991), 667-697. http://ir.lib.sfu.ca/bitstream/1892/9102/1/b15004946.pdf

Further reading

O'Connor, John J.; Robertson, Edmund F., "Shams al-Din Abu Abdallah Al-Khalili", MacTutor History of Mathematics archive, University of St Andrews.
King, David. A. (1970–80). "Khalīlī, Shams al-Dīn Abū ʿAbdallāh Muḥammad Ibn Muḥammad al-". Dictionary of Scientific Biography. New York: Charles Scribner's Sons. ISBN 0684101149.
Denis Roegel: An Extension of Al-Khalīlī's Qibla Table to the Entire World, 2008, INRIA technical report inria-00336090 (available on http://locomat.loria.fr)


Mathematics Encyclopedia

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