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{{Short description|Egyptian mathematician (c. 950–1009)}}
{{Use dmy dates|date=September 2020}}
{{Infobox person
| name               = Ibn Yunus
| image              = 
| birth_name         = Abu al-Hasan 'Ali Abi al-Said ibn 'Abd al-Rahman ibn Ahmad ibn Yunus bin Abd al-'Ala al-Sadafi al-Misri 
({{lang|arz|أبو الحسن علي أبي السعيد بن عبد الرحمن بن أحمد بن يونس بن عبد الأعلى الصدفي المصري}})
| birth_date         = 950
| birth_place        = [[Fustat]], [[Ikhshidid dynasty|Ikhshidid Emirate of Egypt]], now [[Egypt]]
| death_date         = 6 June 1009
| death_place        = [[Cairo]], [[Fatimid Caliphate|Egyptian Fatimid Caliphate]], now [[Egypt]]
| occupation         = [[Astronomer]], [[astrologer]], [[mathematician]], [[philosopher]]
| era                = [[Ikhshidid dynasty|Ikhshidid era]]<br /> [[Abbasid Caliphate|Abbasid era]]<br /> [[Fatimid Caliphate|Fatimid era]]
| notable_works      = * Al-Zij al-Kabir al-Hakimi
* Bulugh al-Umniyya
* Zij ibn Yunus
* Ghayat al-Intifah fi Mareafat al-Da'ir min al-Falak min qabl al-Iritifah
}}

'''Abu al-Hasan 'Ali ibn Abi al-Said 'Abd al-Rahman ibn Ahmad ibn Yunus ibn Abd al-'Ala al-Sadafi al-Misri''' ([[Egyptian Arabic]]: ابن يونس; c. 950 – 1009) was an important [[Arabs|Arab]] [[Egyptians|Egyptian]] astronomer and [[Islamic mathematics|mathematician]],<ref name="KIng">{{cite book  |author1=David King |author1-link=David A. King (historian) |editor1-last=Seling |editor1-first=Helaine |title=Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures |date=12 March 2008 |publisher=Springer Science & Business Media |isbn=978-1-4020-4559-2 |page=1124 |url=https://books.google.com/books?id=kt9DIY1g9HYC&dq=Ibn+Yunus&pg=PA1124 |access-date=16 November 2021 |language=en}}</ref><ref>Science & Technology in the Islamic World - Page 77</ref><ref>Science in Medieval Islam: an illustrated introduction by Howard R. Turner - Page 65</ref> whose works are noted for being ahead of their time, having been based on meticulous calculations and attention to detail. He is one of the famous [[Muslims|Muslim]] astronomers who appeared after [[Al-Battani]] and [[Abu al-Wafa' al-Buzjani]], and he was perhaps the greatest astronomer of his time. Because of his brilliance, the [[Fatimid Caliphate|Fatimids]] gave him generous gifts and established an observatory for him on Mount Mokattam near [[Fustat]]. [[Al-Aziz Billah]] ordered him to make astronomical tables, which he completed during the reign of [[Al-Hakim bi-Amr Allah]], son of Al-Aziz, and called it al-Zij al-Kabir al-Hakimi.<ref>{{Cite web |title=Starry Messenger: Ibn Yunus and Astronomical Tables |url=http://www.sites.hps.cam.ac.uk/starry/ibnyunustables.html |access-date=2024-02-18 |website=www.sites.hps.cam.ac.uk}}</ref><ref>{{Cite web |title=al-Zīj al-kabīr al-Ḥākimī {{!}} ISMI |url=https://ismi.mpiwg-berlin.mpg.de/text/61448 |access-date=2024-02-18 |website=ismi.mpiwg-berlin.mpg.de}}</ref>
The crater [[Ibn Yunus (crater)|Ibn Yunus]] on the [[Moon]] is named after him.
[[File:Ibn_Yunus_eclipses_1004_CE_manuscript_records_Arabic.jpg|thumb|Ibn Yunus' records of the solar eclipses of 993 and 1004 as well as the lunar eclipses of 1001 and 1002.]]

==Life==
Information regarding his early life and education is uncertain. He was born in [[Egypt]] between 950 and 952 and came from a respected family in [[Fustat]]. His father was a historian, biographer, and scholar of [[hadith]] who wrote two volumes about the history of Egypt—one about the [[Egyptians]] and one based on traveller commentary on Egypt.<ref>Eternal Egypt. [http://www.eternalegypt.org/EternalEgyptWebsiteWeb/HomeServlet?ee_website_action_key=action.display.element&story_id=&module_id=&language_id=1&element_id=2019 Ibn Yunus The Historian].</ref> A prolific writer, ibn Yunus' father has been described as "Egypt's most celebrated early historian and first known compiler of a biographical dictionary devoted exclusively to Egyptians".<ref>Eickelman, Dale F. James Piscatori. ''Muslim Travellers: Pilgrimage, Migration, and the Religious Imagination''. Berkeley: University of California Press, 1990. p. 58</ref> His grandfather was also one of the scholars who specialized in astronomy, and Ibn Yunus enjoyed great prestige among the Fatimid caliphs, who encouraged him to pursue his astronomical and mathematical research. They built an observatory for him near Fustat (Cairo), and equipped it with all the necessary machinery and tools. [[George Sarton|Sarton]] says of him that he was perhaps the greatest Muslim astronomer. His great-grandfather had been an associate of the noted legal scholar [[al-Shafi'i]].

Early in the life of ibn Yunus, the [[Fatimid dynasty]] came to power and the new city of [[Cairo]] was founded. In Cairo, he worked as an astronomer for the Fatimid dynasty for twenty-six years, first for the Caliph [[Al-Aziz Billah]] and then for [[Al-Hakim bi-Amr Allah|al-Hakim]]. Ibn Yunus dedicated his most famous astronomical work, ''al-Zij al-Kabir al-Hakimi'', to the latter.

As well as for his mathematics, Ibn Yunus was also known as an eccentric and a poet.<ref>{{citation|title=Episodes in the Mathematics of Medieval Islam|first=J. L.|last=Berggren|publisher=Springer|year=2003|isbn=9780387406053|page=148|url=https://books.google.com/books?id=cDEQ5fH15ucC&pg=PA148}}.</ref>

==Works==
One of his greatest astronomical works was that he calculated with great accuracy the inclination of the ecliptic circle, after observing the solar and lunar eclipses.

Ibn Yunus excelled in trigonometry, and he was the first to solve some of the trigonometric equations that are used in astronomy, and he conducted valuable research in it that helped advance trigonometry. He was the first to establish a law for spherical trigonometry, and it was of great importance to scholars of astronomy, before the discovery of logarithms, since by means of that law multiplication operations in trigonometry could be converted into addition operations, it facilitated the solution of many long and complex problems.

Ibn Yunus showed great ingenuity in solving many difficult problems in astronomy.

Ibn Yunus observed the eclipse of the sun and moon in Cairo in 978 AD, and his calculation came closest to what was known, until modern observing machines appeared.

===Astrology===
{{Noref section|date=July 2021}}
In [[astrology]], noted for making predictions and having written the ''Kitab bulugh al-umniyya'' ("On the Attainment of Desire"), a work concerning the [[heliacal rising]]s of [[Sirius]], and on predictions concerning what day of the week the [[Coptic calendar|Coptic]] year will start on.

===Astronomy===
[[File:Ibn Yunus LROC.jpg|thumb|Ibn Yunus lunar crater, named after him]]
Ibn Yunus' most famous work in [[Islamic astronomy]], ''al-[[Zij]] al-Kabir al-Hakimi'' (c. 1000), was a handbook of astronomical tables which contained very accurate observations, many of which may have been obtained with very large astronomical instruments. According to N. M. Swerdlow, the ''Zij al-Kabir al-Hakimi'' is "a work of outstanding originality of which just over half survives".<ref>N. M. Swerdlow (1993), "Montucla's Legacy: The History of the Exact Sciences", ''Journal of the History of Ideas'' '''54''' (2): 299–328 [320].</ref>

Yunus expressed the solutions in his ''zij'' without mathematical symbols,<ref>[http://www.encyclopedia.com/doc/1G2-2830904759.html Complete Dictionary of Scientific Biography], 2008</ref> but [[Jean Baptiste Joseph Delambre|Delambre]] noted in his 1819 translation of the Hakemite tables that two of Ibn Yunus' methods for determining the time from solar or stellar altitude were equivalent to the [[trigonometric identity]] <math>2\cos(a)\cos(b) = \cos(a+b)+\cos(a-b)</math><ref>David A. King, '[http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1978JHA.....9..212K&db_key=AST&page_ind=6&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES Islamic Math and Science]', Journal for the History of Astronomy, Vol. 9, p.212</ref> identified in [[Johannes Werner]]'s 16th-century manuscript on conic sections.  Now recognized as one of Werner's formulas, it was essential for the development of [[prosthaphaeresis]] and [[logarithms]] decades later.

Ibn Yunus described 40 [[Conjunction (astronomy and astrology)|planetary conjunctions]] and 30 [[lunar eclipse]]s. For example, he accurately describes the planetary conjunction that occurred in the year 1000 as follows:
:A conjunction of Venus and Mercury in Gemini, observed in the western sky: The two planets were in conjunction after sunset on the night [of Sunday 19 May 1000]. The time was approximately eight equinoctial hours after midday on Sunday. Mercury was north of Venus and their latitude difference was a third of a degree.<ref name=MacTutor>{{MacTutor|id=Yunus|title=Abu'l-Hasan Ali ibn Abd al-Rahman ibn Yunus}}</ref>

Modern knowledge of the positions of the planets confirms that his description and his calculation of the distance being one-third of a degree is exactly correct. Ibn Yunus's observations on conjunctions and [[eclipse]]s were used in [[Richard Dunthorne]] and [[Simon Newcomb]]s' respective calculations of the secular acceleration of the [[Moon]].<ref name=MacTutor/><ref>Raymond Mercer (1994), 'English Orientalists and Mathematical Astronomy' in ''The 'Arabick' Interest of the Natural Philosophers in 17th-Century England'', p.198</ref>

===Pendulum===
Recent encyclopaedias<ref>{{cite book
  | last = Good
  | first = Gregory
  | title = Sciences of the Earth: An Encyclopedia of Events, People, and Phenomena
  | publisher = [[Routledge]]
  | date = 1998
  | pages = 394
  | url = https://books.google.com/books?id=vdqXVddh0hUC
  | isbn = 978-0-8153-0062-5}}<br/>{{cite encyclopedia
  | title = Pendulum
  | encyclopedia = Encyclopedia Americana
  | volume = 21
  | pages = 502
  | publisher = The Americana Corp.
  | url =https://books.google.com/books?id=icRWAAAAMAAJ&q=%22Ibn+Yunis%22+pendulum
  | date = 1967
  | access-date = 2009-02-20}}<br/>{{cite book
  | last = Baker
  | first = Cyril Clarence Thomas
  | title = Dictionary of Mathematics
  | publisher = G. Newnes
  | date = 1961
  | pages = 176
  | url = https://books.google.com/books?id=RlkYAAAAMAAJ&q=Ibn+Yunis+pendulum
  }}</ref> and popular accounts<ref>{{cite book|author-link=Roger G. Newton
  | last = Newton
  | first = Roger G.
  | title = Galileo's Pendulum: From the Rhythm of Time to the Making of Matter
  | publisher = [[Harvard University Press]]
  | date = 2004
  | location = US
  | pages = [https://archive.org/details/galileospendulum0000newt/page/52 52]
  | url = https://archive.org/details/galileospendulum0000newt
  |url-access=registration
  | isbn =  978-0-674-01331-5}}</ref> claim that the tenth century astronomer Ibn Yunus used a [[pendulum]] for time measurement, despite the fact that it has been known for nearly a hundred years that this is based on nothing more than an error made in 1684 by the Savilian Professor of Astronomy at Oxford [[Edward Bernard]].<ref>{{cite journal
 | last=King
 | first=D. A.
 | title=Ibn Yunus and the pendulum: a history of errors
 | journal=Archives Internationales d'Histoire des Sciences
 | date=1979
 | volume=29
 | issue=104
 | pages=35–52 }}<br/>
{{cite journal
  | last =  Hall
  | first = Bert S.
  | title = The scholastic pendulum
  | journal =  Annals of Science
  | volume = 35
  | issue = 5
  | pages = 441–462
  | publisher = [[Taylor & Francis]]
  | date = September 1978
  | issn =  0003-3790
  | doi =10.1080/00033797800200371
  }}<br/>
{{cite web
 |author1=O'Connor, J. J. |author2=Robertson, E. F. | date=November 1999
 | url =http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Yunus.html
 | title =Abu'l-Hasan Ali ibn Abd al-Rahman ibn Yunus
 | publisher =[[University of St Andrews]]
 | access-date = 2007-05-29 }}</ref>

== Ibn Yunus's philosophy ==
[[File:Maximum Benefit from the Knowledge of Circles of Projection on the 30 Degree Northern Latitude WDL2854.jpg|thumb|The book “''Ghayat al-Intifah fi Mareafat al-Da'ir min al-Falak min qabl al-Iritifah''” by the scholar Abu Al-Hasan Ali Ibn Yunus]]
In his scientific studies, he only believed in what his mind was convinced of, and he did not care what people said about him. His philosophy was summarized in three points:<ref name=":0">{{Cite web |title=ابن يونس المصري |url=https://areq.net/m/%D8%A7%D8%A8%D9%86_%D9%8A%D9%88%D9%86%D8%B3_%D8%A7%D9%84%D9%85%D8%B5%D8%B1%D9%8A.html |access-date=2024-02-18 |website=areq.net |language=ar}}</ref>

* Adopting the scientific principle based on observation and measurement, and taking the universe and everything in it as a teacher, from which facts are deduced and to which they are returned.<ref name=":0" />
* Strengthening faith by touching the signs of the Creator emanating in the universe.<ref name=":0" />
* Practicing legitimate pleasures. ([[Ibn Khallikan]] mentions about one of the astrologers that he once went with him to Mount Mokattam, and he stopped to observe the planet Venus, so he took off his turban and dress and put on a red shirt and a red mask to cover himself with. He took out a stick and struck it with incense in his hands, and his situation was bizarre).<ref name=":0" />

== Narration of Hadith ==
Ibn Yunus narrated hadiths and reports from his father, Abi al-Sa'id, but the scholars rejected his narration due to his preoccupation with astrology and magic.<ref>[[Al-Dhahabi]], ''المغني في الضعفاء'', investigation: Dr. Nour al-Din Atar, part 2. p. 448</ref>

== Books ==
Ibn Yunus had many works, and his most important book is ''Al-Zij Al-Kabir Al-Hakimi'', which is the book he began writing, by order of the Fatimid Caliph Al-Aziz in the year 380 AH/990 AD, and completed it in 1007 AD during the reign of Caliph Al-Hakim Ould Al-Aziz, and he called it Al-Zij Al-Hakimi, after the caliph.

The word ''Zij'' is a [[Persian language|Persian]] word (Zik), and its meaning in our modern sense is mathematical astronomical tables. He had another book called ''Zij Ibn Yunus'', and the numbers he included in his two ''zij'' books are correct up to the seventh decimal number, which indicates unparalleled mathematical accuracy in calculations, and many astronomers have been transmitted from him, especially after his ''zij'' moved to the East, and the Egyptians relied on their calendars on Ibn Yunus’ ''zij'' for a long period of time.

==References==
{{Reflist|30em}}

==External links==
* {{cite encyclopedia | editor = Thomas Hockey | display-editors = etal | last = King | first = David A. | title=Ibn Yūnus: Abū al-Ḥasan ҁʿAlī ibn ʿAbd al-Raḥmān ibn Aḥmad ibn Yūnus al-Ṣadafī | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | date = 2007 | location = New York | pages = 573–4 | url=http://islamsci.mcgill.ca/RASI/BEA/Ibn_Yunus_BEA.htm | isbn=978-0-387-31022-0}} ([http://islamsci.mcgill.ca/RASI/BEA/Ibn_Yunus_BEA.pdf PDF version])
* {{MacTutor|id=Yunus|title=Abu'l-Hasan Ali ibn Abd al-Rahman ibn Yunus}}
* {{cite encyclopedia | last = King | first = David A. | title=Ibn Yūnus, AbuʿL-Hasan ʿAlī Ibn ʿ Abd Al-Rahmān Ibn Yūnus Al Sadafī  | url=http://www.encyclopedia.com/doc/1G2-2830904759.html |  encyclopedia = [[Dictionary of Scientific Biography|Complete Dictionary of Scientific Biography]] | publisher = [[Encyclopedia.com]] | orig-year=1970-80 | date = 2008 }}
* [http://www.hps.cam.ac.uk/starry/ibnyunus.html Ibn Yunus Biography]

{{Islamic astronomy}}
{{Islamic mathematics}}

{{Authority control}}

{{DEFAULTSORT:Yunus, Ibn}}
[[Category:950s births]]
[[Category:1009 deaths]]
[[Category:10th-century Arab people]]
[[Category:11th-century Arab people]]
[[Category:10th-century mathematicians]]
[[Category:11th-century mathematicians]]
[[Category:Medieval Egyptian astrologers]]
[[Category:Medieval Egyptian astronomers]]
[[Category:Medieval Egyptian mathematicians]]
[[Category:Egyptian Muslims]]
[[Category:Islamic philosophers]]
[[Category:Scientists who worked on qibla determination]]
[[Category:10th-century astronomers]]
[[Category:11th-century astronomers]]
[[Category:10th-century astrologers]]
[[Category:11th-century astrologers]]
[[Category:Scholars from the Fatimid Caliphate]]
[[Category:10th-century Egyptian people]]
[[Category:11th-century Egyptian people]]
[[Category:10th-century people from the Fatimid Caliphate]]
[[Category:11th-century people from the Fatimid Caliphate]]