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Abu Mahmud Hamid ibn Khidr Khojandi (known as Abu Mahmood Khojandi, Alkhujandi or al-Khujandi, Persian: ابومحمود خجندی, c. 940 - 1000) was a Persian 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; a bronze bust of the astronomer is present in a park in modern-day Khujand, now part of Tajikistan.

The few facts about Khujandi's life that are known come from his surviving writings as well as from comments made by Nassereddin Tusi. From 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, intended to determine the Earth's axial tilt ("obliquity of the ecliptic") to high precision.

He determined the axial tilt to be 23°32'19" for the year 994 AD. He noted that measurements by earlier astronomers had found higher values (Indians: 24°; Ptolemy 23° 51') and thus discovered that the axial tilt is not constant but is in fact (currently) decreasing. His measurement of the axial tilt was however about 2 minutes too small, probably due to his heavy instrument settling over the course of the observations.[1][2]

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 spherical law of sines may have also been discovered by Khujandi, but it is uncertain whether he discovered it first, or whether Abu Nasr Mansur, Abul Wafa or Nasir al-Din al-Tusi discovered it first.[3][4]

^ Al-Khujandī, Abū Maḥmūd Ḥāmid Ibn Al-Khiḍr, Complete Dictionary of Scientific Biography, 2008
^ O'Connor, John J.; Robertson, Edmund F., "Abu Mahmud Hamid ibn al-Khidr Al-Khujandi", MacTutor History of Mathematics archive, University of St Andrews.
^ Also the 'sine law' (of geometry and trigonometry, applicable to sperical trigonometry) is attributed, among others, to Alkhujandi. (The three others are Abul Wafa Bozjani, Nasiruddin Tusi and Abu Nasr Mansur). Razvi, Syed Abbas Hasan (1991) A history of science, technology, and culture in Central Asia, Volume 1 University of Peshawar, Peshawar, Pakistan, page 358, OCLC 26317600
^ Bijli suggests that three mathematicians are in contention for the honor, Alkhujandi, Abdul-Wafa and Mansur, leaving out Nasiruddin Tusi. Bijli, Shah Muhammad and Delli, Idarah-i Adabiyāt-i (2004) Early Muslims and their contribution to science: ninth to fourteenth century Idarah-i Adabiyat-i Delli, Delhi, India, page 44, OCLC 66527483


O'Connor, John J.; Robertson, Edmund F., "Abu Mahmud Hamid ibn al-Khidr Al-Khujandi", MacTutor History of Mathematics archive, University of St Andrews.

External links

Brummelen, Glen Van (2007). "Khujandī: Abū Maḥmūd Ḥāmid ibn al‐Khiḍr al‐Khujandī". In Thomas Hockey et al. The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 630–1. ISBN 9780387310220. (PDF version)
Tekeli, Sevim (2008) [1970-80]. "Al-Khujandī, Abū Maḥmūd Ḥāmid Ibn Al-Khiḍr". Complete Dictionary of Scientific Biography. Encyclopedia.com.
History of Islamic Science


Mathematics Encyclopedia

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