Shams al-Dīn Abū ʿAbd Allāh Muḥammad ibn Muḥammad al-Khalīlī (; 1320–1380) was a

Mamluk Mamluk or Mamaluk (; (singular), , ''mamālīk'' (plural); translated as "one who is owned", meaning "slave") were non-Arab, ethnically diverse (mostly Turkic, Caucasian, Eastern and Southeastern European) enslaved mercenaries, slave-so ...

-era Syrian

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

who compiled astronomical tables. He worked for most of his life as a (a religious timekeeper) at the

Umayyad Mosque The Umayyad Mosque (; ), also known as the Great Mosque of Damascus, located in the old city of Damascus, the capital of Syria, is one of the largest and oldest mosques in the world. Its religious importance stems from the eschatological reports ...

Damascus Damascus ( , ; ) is the capital and List of largest cities in the Levant region by population, largest city of Syria. It is the oldest capital in the world and, according to some, the fourth Holiest sites in Islam, holiest city in Islam. Kno ...

. Little is known about his life.

Work

Al-Khalili is known for two sets of

mathematical table Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely u ...

s he constructed, both totalling roughly 30,000 entries. He tabulated all the entries made by the celebrated Egyptian Muslim astronomer

Ibn Yunus Abu al-Hasan 'Ali ibn Abi al-Said 'Abd al-Rahman ibn Ahmad ibn Yunus ibn Abd al-'Ala al-Sadafi al-Misri (Egyptian Arabic: ابن يونس; c. 950 – 1009) was an important Arabs, Arab Egyptians, Egyptian astronomer and Islamic mathematics, math ...

, except for the entries that al-Khalili made himself for the city of

. 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 Spherical astronomy, or positional astronomy, is a branch of observational astronomy used to locate astronomical objects on the celestial sphere, as seen at a particular date, time, and location on Earth. It relies on the mathematical methods of ...

for any given

latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...

. In addition to this, he created a 3,000 entry table that gave the (the direction of the city of

Mecca Mecca, officially Makkah al-Mukarramah, is the capital of Mecca Province in the Hejaz region of western Saudi Arabia; it is the Holiest sites in Islam, holiest city in Islam. It is inland from Jeddah on the Red Sea, in a narrow valley above ...

) for all latitudes and longitudes for all the Muslim countries of the 14th century. The values present in al-Khalili’s tables have been determined to be accurate up to three or four

significant figures Significant figures, also referred to as significant digits, are specific digits within a number that is written in positional notation that carry both reliability and necessity in conveying a particular quantity. When presenting the outcom ...

. It is not known how exactly al-Khalili went about calculating each of his entries.

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