Al-Jayyani
Encyclopedia
Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī (989
, Cordova
, Al-Andalus
– 1079, Jaén
, Al-Andalus
) was a mathematician
, Islamic scholar, and Qadi
from Al-Andalus
(in present-day Spain). 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.
" in its modern form, 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. 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. 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 ratio
s as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced Regiomontanus
.
989
Year 989 was a common year starting on Tuesday of the Julian calendar.- Births :* Adémar de Chabannes, monk and historian * Gisela of Swabia, Holy Roman Empress...
, Cordova
Córdoba, Spain
-History:The first trace of human presence in the area are remains of a Neanderthal Man, dating to c. 32,000 BC. In the 8th century BC, during the ancient Tartessos period, a pre-urban settlement existed. The population gradually learned copper and silver metallurgy...
, Al-Andalus
Al-Andalus
Al-Andalus was the Arabic name given to a nation and territorial region also commonly referred to as Moorish Iberia. The name describes parts of the Iberian Peninsula and Septimania governed by Muslims , at various times in the period between 711 and 1492, although the territorial boundaries...
– 1079, Jaén
Jaén, Spain
Jaén is a city in south-central Spain, the name is derived from the Arabic word Jayyan, . It is the capital of the province of Jaén. It is located in the autonomous community of Andalusia....
, Al-Andalus
Al-Andalus
Al-Andalus was the Arabic name given to a nation and territorial region also commonly referred to as Moorish Iberia. The name describes parts of the Iberian Peninsula and Septimania governed by Muslims , at various times in the period between 711 and 1492, although the territorial boundaries...
) was a mathematician
Islamic mathematics
In the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics or Arabic mathematics, covers the body of mathematics preserved and developed under the Islamic civilization between circa 622 and 1600...
, Islamic scholar, and Qadi
Qadi
Qadi is a judge ruling in accordance with Islamic religious law appointed by the ruler of a Muslim country. Because Islam makes no distinction between religious and secular domains, qadis traditionally have jurisdiction over all legal matters involving Muslims...
from Al-Andalus
Al-Andalus
Al-Andalus was the Arabic name given to a nation and territorial region also commonly referred to as Moorish Iberia. The name describes parts of the Iberian Peninsula and Septimania governed by Muslims , at various times in the period between 711 and 1492, although the territorial boundaries...
(in present-day Spain). Al-Jayyānī wrote important commentaries on Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
's Elements
Euclid's Elements
Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...
and he wrote the first known treatise on spherical trigonometry
Spherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
as a discipline independent from astronomy.
Life
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.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 spherical trigonometrySpherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
" in its modern form, although spherical trigonometry in its ancient Hellenistic form was dealt with by earlier mathematicians such as Menelaus of Alexandria
Menelaus of Alexandria
Menelaus of Alexandria was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines.-Life and Works:...
, who developed Menelaus' theorem
Menelaus' theorem
Menelaus' theorem, named for Menelaus of Alexandria, is a theorem about triangles in plane geometry. Given a triangle ABC, and a transversal line that crosses BC, AC and AB at points D, E and F respectively, with D, E, and F distinct from A, B and C, thenThis equation uses signed lengths of...
to deal with spherical problems. However, E. S. Kennedy
E. S. Kennedy
E. S. Kennedy can refer to :* Edward Shirley Kennedy, alpinist and writer* Edward Stewart Kennedy, historian of science...
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. Al-Jayyānī's work on spherical trigonometry "contains formulae for right-handed triangles
Special right triangles
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45-45-90. This is called an "angle-based" right triangle...
, the general law of sines
Law of sines
In trigonometry, the law of sines is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles...
, and the solution of a spherical triangle by means of the polar triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
." This treatise later had a "strong influence on European mathematics", and his "definition of ratio
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...
s as numbers" and "method of solving a spherical triangle when all sides are unknown" are likely to have influenced Regiomontanus
Regiomontanus
Johannes Müller von Königsberg , today best known by his Latin toponym Regiomontanus, was a German mathematician, astronomer, astrologer, translator and instrument maker....
.