Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī ( ar, أبو عبد الله محمد بن معاذ الجياني; 989, Cordova,

Al-Andalus Al-Andalus translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label= Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, al-Ándalus () was the M ...

– 1079, Jaén,

) was an

Arab The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, ...

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, structure, space, models, and change. History On ...

Islamic scholar In Islam, the ''ulama'' (; ar, علماء ', singular ', "scholar", literally "the learned ones", also spelled ''ulema''; feminine: ''alimah'' ingularand ''aalimath'' lural are the guardians, transmitters, and interpreters of religious ...

, and

Qadi A qāḍī ( ar, قاضي, Qāḍī; otherwise transliterated as qazi, cadi, kadi, or kazi) is the magistrate or judge of a '' sharīʿa'' court, who also exercises extrajudicial functions such as mediation, guardianship over orphans and mino ...

from

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

Euclid Euclid (; grc-gre, Εὐκλείδης; 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 ...

'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 sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...

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 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 especially strong ties to etymology). Philology is also defined ...

, and expert in inheritance laws (farāʾiḍī). It is unknown whether they are the same person.

''The book of unknown arcs of a sphere''

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 (; grc-gre, Μενέλαος ὁ Ἀλεξανδρεύς, ''Menelaos ho Alexandreus''; c. 70 – 140 CE) was a Greek Encyclopædia Britannica "Greek mathematician and astronomer who first conceived and defined a spher ...

, who developed

Menelaus' theorem Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ''ABC'', and a transversal line that crosses ''BC'', ''AC'', and ''AB'' at points ''D'', ''E'', and ''F'' respec ...

to deal with spherical problems. 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. (

cf. The abbreviation ''cf.'' (short for the la, confer/conferatur, both meaning "compare") is used in writing to refer the reader to other material to make a comparison with the topic being discussed. Style guides recommend that ''cf.'' be used onl ...

, in ) Al-Jayyānī's work on spherical trigonometry "contains formulae for right-handed triangles, the general

law of sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, \frac \,=\, \frac \,=\, \frac \,=\, 2R, where , and ar ...

, 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 A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...

." 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 ...

Notes

References

*
PDF version
* * 989 births 1079 deaths Astronomers of Al-Andalus Mathematicians of Al-Andalus 11th-century mathematicians 11th-century Al-Andalus people Scientists who worked on qibla determination Mathematicians who worked on Islamic inheritance {{europe-mathematician-stub

Life

''The book of unknown arcs of a sphere''

See also

Notes

References