Person: Mansur, Abu Nasr ibn Ali ibn Iraq
Abu Nasr Mansur was an Islamic prince and mathematician who collaborated with al-Biruni on astronomy and mathematics. He discovered the sine rule for triangles.
Mathematical Profile (Excerpt):
- Abu Nasr Mansur was teaching in this area when he first began his association with al-Biruni whom he taught from about 990.
- The end of the 10th century and beginning of the 11th century was a period of great unrest in the Islamic world and there were civil wars in the region in which Abu Nasr Mansur was living.
- In 995 the Banu Iraq, of which Abu Nasr Mansur was a prince, was overthrown in a coup.
- It is not clear what happened to Abu Nasr Mansur at this stage but certainly his pupil al-Biruni fled at the outbreak of the civil war.
- Not only did Abu Nasr Mansur work there but from about 1004 al-Biruni also worked there, renewing the collaboration between him and his teacher.
- The wars in the region, however, were to disrupt the scientific work of Abu Nasr Mansur and eventually he and al-Biruni left in about 1017.
- Both Abu Nasr Mansur and al-Biruni seem to have left with the victorious Mahmud.
- It seems that Abu Nasr Mansur spent most of the rest of his life at Mahmud's court in Ghazna.
- Abu Nasr Mansur is perhaps most famous for his collaboration with al-Biruni.
- Certainly Abu Nasr Mansur worked on many topics as a result of requests from al-Biruni and a total of twenty-five works are known to have been written by him.
- Seventeen works have survived and they show that Abu Nasr Mansur was an extremely able astronomer and mathematician.
- Of Abu Nasr Mansur's works seven are on mathematics, the rest are on astronomy.
- Many of Abu Nasr Mansur's works were dedicated to his student al-Biruni.
- Al-Biruni himself lists twelve works which he says Abu Nasr Mansur dedicated to him (although some historians read al-Biruni's words as meaning that he wrote the works himself, but this interpretation seems highly unlikely).
- The first such work which Abu Nasr Mansur dedicated to al-Biruni was written around 997, soon after the civil war had disrupted their work.
- In his own writings al-Biruni sometimes quotes results due to Abu Nasr Mansur which he says he worked on at al-Biruni's request.
- Abu Nasr Mansur's main achievements are his commentry on the Spherics of Menelaus, his role in the development of trigonometry from Ptolemy's calculation with chords towards the trigonometric functions used today, and his development of a set of tables which give easy numerical solutions to typical problems of spherical astronomy.
- Abu Nasr Mansur's reworking of the Spherics of Menelaus is particularly important since the Greek original of Menelaus work has been lost, although there are several Arabic versions.
- Abu'l-Wafa may have discovered this law first and Abu Nasr Mansur may have learnt it from him.
- Abu Nasr Mansur's treatise discusses the five trigonometric functions which are used to solve problems in spherical astronomy.
- The article shows the improvement achieved by Abu Nasr Mansur in using 1 as the value of the radius, instead of 60 as was done by most Arabic astronomers.
- Other work by Abu Nasr Mansur on astronomical topics included four works on the construction and application of the astrolabe.
Born 970, (possibly) Khwarazm (now Kara-Kalpakskaya, Uzbekistan). Died 1036, (probably) Ghazna (now Ghazni, Afganistan).
View full biography at MacTutor
Tags relevant for this person:
Ancient Arab, Astronomy, Geography, Origin Uzbekistan
Mentioned in:
Epochs: 1 2
Thank you to the contributors under CC BY-SA 4.0! 
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
