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Abu-mahmud Khojandi Information

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.

Contents

Astronomy

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]

Mathematics

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]

Notes

  1. ^ Al-Khujandī, Abū Maḥmūd Ḥāmid Ibn Al-Khiḍr, Complete Dictionary of Scientific Biography, 2008
  2. ^ O'Connor, John J.; Robertson, Edmund F., "Abu Mahmud Hamid ibn al-Khidr Al-Khujandi", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Khujandi.html .
  3. ^ 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
  4. ^ 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

References

External links

· · Astronomy in medieval Islam
Astronomers
8th century Ahmad NahavandiAl-Fadl ibn NaubakhtIbrāhīm al-Fazārī and his sonMashallah ibn Athari
9th century Abu Ma'shar al-BalkhiAbu Said GorganiAl-FarghānīAl-KindiAl-MahaniAl-Ḥajjāj ibn Yūsuf ibn MaṭarAl-Marwazi'Ali ibn 'Isa al-AsturlabiBanu Musa BrothersIranshahriKhālid ibn ʿAbd al‐MalikAl-KhwārizmīSahl ibn BishrThābit ibn QurraYaʿqūb ibn Ṭāriq
10th century Abd al-Rahman al-SufiAbu-Mahmud KhojandiAbū Ja'far al-KhāzinAbū Sahl al-QūhīAbū al-Wafā' BūzjānīAhmad ibn YusufAl-BattaniAl-NayriziAl-SaghaniIbn YunusIbrahim ibn Sinan
11th century Abu Nasr MansurAl-BīrūnīAl-ZarqālīAlhazenAvicennaIbn al-SaffarKushyar ibn LabbanSaid Al-AndalusiSijzi
12th century Al-BitrujiAl-KharaqīAl-KhaziniAl-Samaw'alAnvariIbn al-KammadJabir ibn AflahOmar KhayyámSharaf al-Dīn al-Ṭūsī
13th century Ibn al-Banna al-MarrakushiIbn al‐Ha'im al‐IshbiliJamal ad-DinMuhyi al-Dīn al-MaghribīNasir al-Din al-TusiQotb al-Din ShiraziShams al-Dīn al-SamarqandīZakariya al-QazwiniIbn Abi al-ShukrMu'ayyad al-Din al-'Urdi
14th century Ibn al-ShatirKamāl al-Dīn FārisīShams al-Dīn Abū Abd Allāh al-Khalīlī
15th century Ali QushjiJamshīd al-KāshīQāḍī Zāda al-RūmīUlugh BegSibt al-Mardini
16th century Al-BirjandiBahāʾ al-dīn al-ʿĀmilīPiri ReisTaqi al-Din Muhammad ibn Ma'ruf
Works ʿAjā'ib al-makhlūqāt wa gharā'ib al-mawjūdāt · Arabic star names · Book of Optics · Encyclopedia of the Brethren of Purity · Islamic calendar · Star chart · Tabula Rogeriana · The Book of Healing Zij: Alfonsine tables · Almanac · Astronomical catalog · Book of Fixed Stars · Star catalogue · Toledan Tables · Trigonometry table · Zij-i Ilkhani · Zij-i-Sultani
Instruments Alidade · Analog computer · Aperture · Armillary sphere · Astrolabe · Astronomical clock · Celestial globe · Compass · Compass rose · Dioptra · Equatorial ring · Equatorium · Globe · Graph paper · Magnifying glass · Mural instrument · Navigational astrolabe · Nebula · Planisphere · Quadrant · Sextant · Shadow square · Spherical astrolabe · Sundial · Telescope · Triquetrum
Concepts Almucantar · Apogee · Astrophysics · Axial tilt · Azimuth · Celestial mechanics · Celestial spheres · Circular orbit · Deferent and epicycle · Earth's rotation · Eccentricity · Ecliptic · Elliptic orbit · Equant · Galaxy · Geocentrism · Gravitational potential energy · Gravity · Heliocentrism · Inertia · Islamic cosmology · Moonlight · Multiverse · Muslim views on astrology · Obliquity · Parallax · Precession · Qibla · Salat times · Specific gravity · Spherical Earth · Starlight · Sublunary sphere · Sunlight · Supernova · Temporal finitism · Trepidation · Triangulation · Tusi-couple · Universe
Centers Al-Azhar University · House of Knowledge · House of Wisdom · Islamic observatories · Istanbul observatory of Taqi al-Din · Madrasah · Maragheh observatory · Observatory · Research institute · Samarkand observatory · Umayyad Mosque · University of Al-Karaouine
Influences

Babylonian astronomy · Egyptian astronomy · Hellenistic astronomy · Indian astronomy

Influenced Byzantine astronomy · Chinese astronomy · European astronomy · Indian astronomy
· · Mathematics in medieval Islam
Mathematicians
9th century 'Abd al-Hamīd ibn Turk · Sind ibn Ali · Al-Abbās ibn Said al-Jawharī · Al-Ḥajjāj ibn Yūsuf ibn Maṭar · Al-Kindi · Al-Mahani · Banū Mūsā · Hunayn ibn Ishaq · Muḥammad ibn Mūsā al-Khwārizmī · Thābit ibn Qurra · Na'im ibn Musa · Sahl ibn Bishr · Habash al-Hasib al-Marwazi
10th century Abd al-Rahman al-Sufi · Abū al-Wafā' al-Būzjānī · Abū Ja'far al-Khāzin · Abū Kāmil Shujāʿ ibn Aslam · Abu'l-Hasan al-Uqlidisi · Abu-Mahmud Khojandi · Ahmad ibn Yusuf · Al-Nayrizi · Al-Saghani · Brethren of Purity · Ibn Sahl · Ibn Yunus · Ibrahim ibn Sinan · Muhammad ibn Jābir al-Harrānī al-Battānī · Sinan ibn Thabit · Al-Isfahani · Abu-Mahmud Khojandi · Nazif ibn Yumn · Abū Sahl al-Qūhī
11th century Abū Ishāq Ibrāhīm al-Zarqālī · Abu Nasr Mansur · Abū Rayḥān al-Bīrūnī · Alhazen · Ibn Muʿādh al-Jayyānī · Al-Karaji · Al-Sijzi · Alī ibn Ahmad al-Nasawī · Avicenna · Ibn Tahir al-Baghdadi · Kushyar ibn Labban · Yusuf al-Mu'taman ibn Hud
12th century Al-Khazini · Ibn Yahyā al-Maghribī al-Samaw'al · Omar Khayyám · Jabir ibn Aflah
13th century Muhyi al-Dīn al-Maghribī · Nasīr al-Dīn al-Tūsī · Shams al-Dīn al-Samarqandī · Sharaf al-Dīn al-Tūsī · Ibn al‐Ha'im al‐Ishbili · Ibn Abi al-Shukr
14th century Yaʿīsh ibn Ibrāhīm al-Umawī · Ibn al-Banna' al-Marrakushi · Ibn al-Shatir · Kamāl al-Dīn Fārisī · Al-Khalili · Qotb al-Din Shirazi · Ahmad al-Qalqashandi
15th century Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī · Ali Qushji · Jamshīd al-Kāshī · Qāḍī Zāda al-Rūmī · Ulugh Beg ·
16th century Al-Birjandi · Muhammad Baqir Yazdi · Taqi al-Din · Ibn Hamza al-Maghribi · Ibn Ghazi al-Miknasi
Treatises Almanac · Book of Fixed Stars · Book of Optics · De Gradibus · Encyclopedia of the Brethren of Purity · Tables of Toledo · Tabula Rogeriana · The Compendious Book on Calculation by Completion and Balancing · The Book of Healing · Zij · Zij-i Ilkhani · Zij-i-Sultani
Concepts Alhazen's problem
Centers Al-Azhar University · Al-Mustansiriya University · House of Knowledge · House of Wisdom · Istanbul observatory of Taqi al-Din · Madrasah · Maktab · Maragheh observatory · University of Al-Karaouine
Influences Babylonian mathematics · Greek mathematics · Indian mathematics
Influenced Byzantine mathematics · European mathematics · Indian mathematics
· · Scholars of Khorasan
Scientists: Abu Ma'shar · Abu Wafa · Abu Zayd Balkhi · Alfraganus · Ali Qushji · Avicenna · Birjandi · Biruni · Hāsib Marwazī · Ibn Hayyān · Khāzin · Khāzinī · Khujandi · Khwarizmi · Nasawi · Nasir al-Din Tusi · Omar Khayyám · Sharaf al-Din Tusi · Sijzi
Philosophers: Algazel · Amiri · Avicenna · Farabi · Nasir Khusraw · Qushayri · Sejestani · Shahrastani
Islamic Scholars: Abu Dawood · Abu Hanifa · Ahmad ibn Hanbal · Ansari · Baghavi · Bayhaqi · Bukhari · Ghazali · Hākim Nishapuri · Juwayni · Malik ibn Dinar · Maturidi · Muslim ibn al-Hajjaj · Nasa'i · Qushayri · Razi · Shaykh Tusi · Taftazani · Tirmizi · Zamakhshari
Poets & Artists: Abu al-Khair · Attar · Behzad · Daqiqi · Ferdowsi · Jami · Rabi'a Balkhi · Rudaki · Rumi · Sanā'ī
Historians & Political figures: Abul-Fazl Bayhaqi · Abu Muslim Khorasani · Abu Saʿīd Gardēzī · Ali Sher Nava'i · Ata al-Mulk Juvayni · Aufi · Bal'ami · Gawhar Shad · Ibn Khordadbeh · Khalid ibn Barmak · Nizam al-Mulk · Tahir Foshanji · Yahya Barmaki
Persondata
Name Khujandi
Alternative names
Short description
Date of birth 940
Place of birth
Date of death 1000
Place of death

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