**Al-Khazin** was an Islamic mathematician who worked on number theory and astronomy.

- As far as this article is concerned we will assume that al-Khazin worked on both topics.
- The Buyid dynasty, ruling in western Iran and Iraq, reach its peak around the time that al-Khazin lived.
- Al-Khazin was one of the scientists brought to the court in Rayy by the ruler of the Buyid dynasty, Adud ad-Dawlah, who ruled from 949 to 983.
- We know that in 959/960 al-Khazin was required by the vizier of Rayy, who was appointed by Adud ad-Dawlah, to measure the obliquity of the ecliptic (the angle which the plane in which the sun appears to move makes with the equator of the earth).
- One of al-Khazin's works Zij al-Safa'ih (Tables of the disks of the astrolabe) was described by his successors as the best work in the field and they make many reference to it.
- Al-Khazin wrote a commentary on Ptolemy's Almagest Ⓣ(The major thesis: from the Arabic 'al-majisti' -- the Arabic translation of the Greek 'Mathematike Syntaxis' later translated into Latin as 'Magna Syntaxis') which was criticised by al-Biruni for being too verbose.
- The fragment which has survived contains a discussion by al-Khazin of Ptolemy's argument that the universe is spherical.
- Al-Khazin gives 19 propositions relating to this statement by Ptolemy.
- When he tries to generalise this result to polygons, however, al-Khazin gives incorrect proofs.
- The work of al-Khazin which is described seems to have been motivated by work of a mathematician by the name of al-Khujandi.
- This seems to have motivated further correspondence on number theory between al-Khazin and other Arabic mathematicians.
- Results by al-Khazin here are interesting indeed.
- Rashed has discovered a manuscript which appears to be by al-Khazin, yet contains exactly what he had attributed to al-Khujandi.
- Although al-Khazin could have realised the error in al-Khujandi's proof and attempted a similar proof himself which he believed correct, there is no really satisfactory explanation of these facts.
- Finally we should mention that al-Khazin proposed a different solar model from that of Ptolemy.
- Al-Khazin was unhappy with this model since he claimed that if this were the case then the apparent diameter of the sun would vary throughout the year and observation showed that this were not the case.
- Of course the apparent diameter of the sun does vary but by too small an amount to be observed by al-Khazin.
- To get round this problem, al-Khazin proposed a model in which the sun moved in a circle which was centred on the earth, but its motion was not uniform about the centre, rather it was uniform about another point (called the excentre).

Born about 900, Khurasan (eastern Iran). Died about 971, possibly Rayy.

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Ancient Arab, Astronomy, Origin Iran

Epochs: 1

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive