Al-Jayyani
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Abu Abd Allah Muhammad ibn Muadh Al-Jayyani, shortened to Al-Jayyani (989, Cordova, Al-Andalus – 1079, Jaen, Al-Andalus) was an Arab mathematician from Al-Andalus (in present-day Spain). Al-Jayyani wrote important commentaries on Euclid's Elements and he wrote the first treatise on spherical trigonometry in its modern form. Little is known about his life. Confusion exists over the identity of Al-Jayyani the scholar and Al-Jayyani the mathematician. It is unknown whether they are the same person.
[edit] The book of unknown arcs of a sphere
Al-Jayyani The book of unknown arcs of a sphere, which is considered "the first treatise on spherical trigonometry" in its modern form,[1] 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.[2] 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.[3] Al-Jayyani'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.[1]
[edit] See also
[edit] References
- ^ a b O'Connor, John J.; Robertson, Edmund F., "Abu Abd Allah Muhammad ibn Muadh Al-Jayyani", MacTutor History of Mathematics archive.
- ^ O'Connor, John J.; Robertson, Edmund F., "Menelaus of Alexandria", MacTutor History of Mathematics archive. "Book 3 deals with spherical trigonometry and includes Menelaus's theorem."
- ^ Kennedy, E. S. (1969), "The History of Trigonoemetry", 31st Yearbook (National Council of Teachers of Mathematics, Washington DC): 337 (cf. Haq, Syed Nomanul, The Indian and Persian background, p. 68, in Seyyed Hossein Nasr, Oliver Leaman (1996), History of Islamic Philosophy, Routledge, pp. 52–70, ISBN 0415131596)
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