Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī (; 989, Cordova,

Al-Andalus Al-Andalus () was the Muslim-ruled area of the Iberian Peninsula. The name refers to the different Muslim states that controlled these territories at various times between 711 and 1492. At its greatest geographical extent, it occupied most o ...

– 1079, Jaén,

) was an

Arab Arabs (, , ; , , ) are an ethnic group mainly inhabiting the Arab world in West Asia and North Africa. A significant Arab diaspora is present in various parts of the world. Arabs have been in the Fertile Crescent for thousands of years ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

Islamic scholar In Islam, the ''ulama'' ( ; also spelled ''ulema''; ; singular ; feminine singular , plural ) are scholars of Islamic doctrine and law. They are considered the guardians, transmitters, and interpreters of religious knowledge in Islam. "Ulama ...

, and

Qadi A qadi (; ) is the magistrate or judge of a Sharia court, who also exercises extrajudicial functions such as mediation, guardianship over orphans and minors, and supervision and auditing of public works. History The term '' was in use from ...

from

(in present-day Spain). Al-Jayyānī wrote important commentaries on

Euclid Euclid (; ; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of geometry that largely domina ...

's '' Elements'' and he wrote the first known treatise on

spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, ge ...

Life

Little is known about his life. Confusion exists over the identity of ''al-Jayyānī'' of the same name mentioned by ibn Bashkuwal (died 1183),

Qur'anic The Quran, also Romanization, romanized Qur'an or Koran, is the central religious text of Islam, believed by Muslims to be a Waḥy, revelation directly from God in Islam, God (''Allah, Allāh''). It is organized in 114 chapters (, ) which ...

scholar, Arabic

Philologist Philology () is the study of language in oral and written historical sources. It is the intersection of textual criticism, literary criticism, history, and linguistics with strong ties to etymology. Philology is also defined as the study of ...

, and expert in inheritance laws (farāʾiḍī). It is unknown whether they are the same person. There is some evidence that he lived in

Cairo Cairo ( ; , ) is the Capital city, capital and largest city of Egypt and the Cairo Governorate, being home to more than 10 million people. It is also part of the List of urban agglomerations in Africa, largest urban agglomeration in Africa, L ...

from 1012/13 to 1016/17.

Works

Al-Jayyānī wrote ''The book of unknown arcs of a sphere'', which is considered "the first treatise on

", although spherical trigonometry in its ancient Hellenistic form was dealt with by earlier mathematicians such as

Menelaus of Alexandria Menelaus of Alexandria (; , ''Menelaos ho Alexandreus''; c. 70 – 140 CE) was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines. Life and works Although very li ...

, whose treatise the ''Spherics'' included

Menelaus' theorem In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle , and a Transversal (geometry), transversal line that crosses at points respectively, wi ...

, still a basic tool for solving spherical geometry problems in Al-Jayyānī's time. However, E. S. Kennedy points out that while it was possible in pre-Islamic mathematics to compute the magnitudes of a spherical figure, in principle, by use of the table of chords and Menelaus' theorem, the application of the theorem to spherical problems was very difficult in practice. Al-Jayyānī's work on spherical trigonometry "contains formulae for right-handed triangles, the general

law of sines In trigonometry, the law of sines (sometimes called the sine formula or sine rule) is a mathematical equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, \frac \,=\, \frac \,=\, \frac \,=\ ...

, and the solution of a

spherical triangle Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are gre ...

by means of the

polar triangle Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...

." This treatise later had a "strong influence on European mathematics", and his "definition of

ratio In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...

s as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced

Regiomontanus Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrument ...

. There is strong consensus in attributing the authorship of a manuscript about the duration of twilight to him. The short treatise ''On twilight'' was incorrectly attributed to

Ibn al-Haytham Ḥasan Ibn al-Haytham (Latinization of names, Latinized as Alhazen; ; full name ; ) was a medieval Mathematics in medieval Islam, mathematician, Astronomy in the medieval Islamic world, astronomer, and Physics in the medieval Islamic world, p ...

for several centuries, due to a reference made by

Gerard of Cremona Gerard of Cremona (Latin: ''Gerardus Cremonensis''; c. 1114 – 1187) was an Italians, Italian translator of scientific books from Arabic into Latin. He worked in Toledo, Spain, Toledo, Kingdom of Castile and obtained the Arabic books in the libr ...

, who translated it into Latin. The first printed edition of Cremona's translation (''Allacen arabis uetustissimi liber de crepusculis, Gerardo Cremonensi interprete'') was made in 1542, by the Portuguese mathematician and cosmographer

Pedro Nunes Pedro Nunes (; Latin: ''Petrus Nonius''; 1502 – 11 August 1578) was a Portuguese mathematician, cosmographer, and professor, probably from a New Christian (of Jewish origin) family.Leitão, Henrique, "Para uma biografia de Pedro Nunes: O ...

Notes

References

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* * {{DEFAULTSORT:Jayyani, Ibn Muahd 989 births 1079 deaths Astronomers from al-Andalus Mathematicians from al-Andalus 11th-century mathematicians 11th-century people from al-Andalus Scientists who worked on qibla determination Mathematicians who worked on Islamic inheritance

Life

Works

See also

Notes

References