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**Abu al-Hasan 'Ali ibn 'Abd al-Rahman ibn Ahmad ibn Yunus al-Sadafi al-Misri** (Arabic: ابن يونس; c. 950 – 1009) was an important Egyptian Muslim astronomer and mathematician,^{[1]}^{[2]}^{[3]}^{[4]} whose works are noted for being ahead of their time, having been based on meticulous calculations and attention to detail.

The crater Ibn Yunus on the Moon is named after him.

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.^{[5]} 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".^{[6]} His great-grandfather had been an associate of the noted legal scholar Imam Shafi.

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 and then for 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.^{[7]}

In astrology, noted for making predictions and having written the *Kitab bulugh al-umniyya* ("On the Attainment of Desire"), a work concerning the heliacal risings of Sirius, and on predictions concerning what day of the week the Coptic year will start on.

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".^{[8]}

Yunus expressed the solutions in his *zij* without mathematical symbols,^{[9]} but 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 ^{[10]} 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 planetary conjunctions and 30 lunar eclipses. 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.
^{[11]}

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 eclipses were used in Richard Dunthorne and Simon Newcombs' respective calculations of the secular acceleration of the moon.^{[11]}^{[12]}

Recent encyclopaedias^{[13]} and popular accounts^{[14]} 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.^{[15]}

**^**Ivan van Sertima,*Egypt: Child of Africa*, p. 337.**^**Science & Technology in the Islamic World - Page 77**^**Science in Medieval Islam: an illustrated introduction by Howard R. Turner - Page 65**^**Eternal Egypt. Ibn-Yunus El-Falaky Archived 16 July 2011 at the Wayback Machine.**^**Eternal Egypt. Ibn Yunus The Historian.**^**Eickelman, Dale F. James Piscatori.*Muslim Travellers: Pilgrimage, Migration, and the Religious Imagination*. Berkeley: University of California Press, 1990. p. 58**^**Berggren, J. L. (2003),*Episodes in the Mathematics of Medieval Islam*, Springer, p. 148, ISBN 9780387406053.**^**N. M. Swerdlow (1993), "Montucla's Legacy: The History of the Exact Sciences",*Journal of the History of Ideas***54**(2): 299-328 [320].**^**Complete Dictionary of Scientific Biography, 2008**^**David A. King, 'Islamic Math and Science', Journal for the History of Astronomy, Vol. 9, p.212- ^
^{a}^{b}O'Connor, John J.; Robertson, Edmund F., "Abu'l-Hasan Ali ibn Abd al-Rahman ibn Yunus",*MacTutor History of Mathematics archive*, University of St Andrews. **^**Raymond Mercer (1994), 'English Orientalists and Mathematical Astronomy' in*The 'Arabick' Interest of the Natural Philosophers in 17th-Century England*, p.198**^**Good, Gregory (1998).*Sciences of the Earth: An Encyclopedia of Events, People, and Phenomena*. Routledge. p. 394. ISBN 978-0-8153-0062-5.

"Pendulum".*Encyclopedia Americana*.**21**. The Americana Corp. 1967. p. 502. Retrieved 20 February 2009.

Baker, Cyril Clarence Thomas (1961).*Dictionary of Mathematics*. G. Newnes. p. 176.**^**Newton, Roger G. (2004).*Galileo's Pendulum: From the Rhythm of Time to the Making of Matter*. US: Harvard University Press. p. 52. ISBN 978-0-674-01331-5.**^**King, D. A. (1979). "Ibn Yunus and the pendulum: a history of errors".*Archives Internationales d'Histoire des Sciences*.**29**(104): 35–52.

Hall, Bert S. (September 1978). "The scholastic pendulum".*Annals of Science*. Taylor & Francis.**35**(5): 441–462. doi:10.1080/00033797800200371. ISSN 0003-3790.

O'Connor, J. J.; Robertson, E. F. (November 1999). "Abu'l-Hasan Ali ibn Abd al-Rahman ibn Yunus". University of St Andrews. Retrieved 29 May 2007.

- King, David A. (2007). "Ibn Yūnus: Abū al‐Ḥasan ҁʿAlī ibn ʿAbd al‐Raḥmān ibn Aḥmad ibn Yūnus al‐Ṣadafī". In Thomas Hockey; et al. (eds.).
*The Biographical Encyclopedia of Astronomers*. New York: Springer. pp. 573–4. ISBN 978-0-387-31022-0. (PDF version) - O'Connor, John J.; Robertson, Edmund F., "Abu'l-Hasan Ali ibn Abd al-Rahman ibn Yunus",
*MacTutor History of Mathematics archive*, University of St Andrews. - King, David A. (2008) [1970-80]. "Ibn Yūnus, AbuʿL-Hasan ʿAlī Ibn ʿ Abd Al-Rahmān Ibn Yūnus Al Sadafī".
*Complete Dictionary of Scientific Biography*. Encyclopedia.com. - Ibn Yunus Biography