| Full name | Al-Jayyānī |
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| Born | 989 AD Cordova, Al-Andalus |
| Died | 1079 AD Jaén, Al-Andalus |
| Era | Islamic Golden Age |
| Region | Islamic civilization |
| Main interests | Mathematics, Astronomy |
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Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī[1] (989, Cordova, Al-Andalus – 1079, Jaén, Al-Andalus) was a mathematician, Islamic scholar, and Qadi from Al-Andalus (in present-day Spain).[2] Al-Jayyānī wrote important commentaries on Euclid's Elements and he wrote the first known treatise on spherical trigonometry as a discipline independent from astronomy.
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Little is known about his life. Confusion exists over the identity of al-Jayyānī of the same name mentioned by ibn Bashkuwal (d. 1183), Qur'anic scholar, Arabic Philologist, and expert in inheritance laws (farāʾiḍī). It is unknown whether they are the same person.[3]
Al-Jayyānī wrote The book of unknown arcs of a sphere, which is considered "the first treatise on spherical trigonometry" in its modern form,[4] although spherical trigonometry in its ancient Hellenistic form was dealt with by earlier mathematicians such as Menelaus of Alexandria, who developed Menelaus' theorem to deal with spherical problems.[5] However, E. S. Kennedy points out that while it was possible in pre-lslamic 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.[6] Al-Jayyānī's work on spherical trigonometry "contains formulae for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle." This treatise later had a "strong influence on European mathematics", and his "definition of ratios as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced Regiomontanus.[4]
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