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Abu-Mahmud al-Khujandi

Abu Mahmood Khujandi or Abu Mahmud Hamid ibn al-Khidr Al-Khujandi (Persian: ابومحمود خجندی) was a Turkic astronomer and mathematician who lived in the late 10th century and helped build an observatory near the city of Ray (near today's Tehran) in Iran. He was born in Khujand (now Tajikistan) about 940 and died in 1000.

The few facts about Khujandi's life that are known come from both his surviving writings and comments made by Nassereddin Tusi. Useful Reference Encyclopedia Tusi's comments it is fairly certain that Khujandi was one of the rulers of the Mongol tribe in the Khudzhand region, and thus must have come from the nobility.



In Islamic astronomy, Khujandi worked under the patronage of the Buwayhid Amirs at the observatory near Ray, Iran, where he is known to have constructed the first huge mural sextant in 994 AD.[1]

Al-Khujandi determined the axial tilt to be 23°32'19" (23.53°)[2] for the year 994 AD.


In Islamic mathematics, he stated a special case of Fermat's last theorem for n = 3, but his attempted proof of the theorem was incorrect. The law of sines may have also been discovered by Khujandi, but it is uncertain whether he discovered it first, or whether Abu Nasr Mansur or Abul Wafa discovered it first.


  1. ^ O'Connor, John J.; Robertson, Edmund F., "Abu Mahmud Hamid ibn al-Khidr Al-Khujandi", MacTutor History of Mathematics archive .
  2. ^ Richard P. Aulie (1994), "Al-Ghazali Contra Aristotle: An Unforeseen Overture to Science In Eleventh-Century Baghdad", PSCF 45: 26-46 (cf. References, 1001 Inventions)


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