Since the establishment of Islam in the early 7th century, it has rapidly formed a powerful force, and rapidly expanded to a vast area outside the Arabian Peninsula, spanning three continents: Europe, Asia and Africa. In this vast area, Arabic is the common official language, and Arabic mathematics here refers to mathematics learned in Arabic.
Since the eighth century, it takes about one to one and a half centuries to translate Arabic mathematics. Baghdad has become an academic center with a science palace, an observatory, a library and a college. Scholars from all over the world have translated a large number of classical works from Greece, India and Persia into Arabic. In the process of translation, many documents have been revised, verified and supplemented, and a large number of ancient mathematical heritages have been reborn. On the basis of accepting foreign cultures, Arab civilization and culture developed rapidly, and remained vigorous until the15th century. Arabic mathematics, with the rise and fall of Arab science in the whole Middle Ages, can be roughly divided into three periods.
From the 8th century to the middle of the 9th century, the Abbasid dynasty established the "Wisdom Palace" in Baghdad, with an observatory and a library attached, where many scholars from Persia, Syria, Egypt and India gathered. This period is the introductory period of translation-oriented mathematical knowledge. Euclid's Elements of Geometry was written for the first time. Soon after, the works of Indian mathematician Brahmaguta were also translated into Arabic. Later, the works of ancient Greek mathematicians such as Archimedes, Apollonius, Diophantine and Ptolemy were also translated into Arabic. The famous mathematician in this period was Walter Mill. In addition to his translation and annotation work, he also wrote famous works, such as algie Barra and Al Mukabara (meaning "science of reduction and cancellation") and Hua Lamizishu (known as "Liber Algorismi" in many Latin scientific works). The commonly used terms "algebra" and "algorithm" are derived from the titles of these two books.
From the middle of 9th century to13rd century, Arabic mathematics flourished. During this period, many academic research centers appeared in Baghdad, Bukhara, Cairo, Cordoba, Toledo and other places in Spain. Famous mathematicians in this period include Albategnius, Abu Wafa, Karaki, biruni, Ou Ma khayyam, Nasir Din Tutsi, Banna and others.
/kloc-After the 4th century, the whole Arabic mathematics was in decline, except Samarkand Observatory of Jamir Dynasty and Kathy who worked there in the 5th century.
The main achievements of Arabic mathematics in arithmetic are: decimal number system, written calculation (both of which are influenced by India), raising the power of higher order, and summing formulas of several series. Algebra includes: solutions of linear and quadratic equations (shifting and merging at both ends of the equation), geometric solutions of cubic equations, and coefficient tables of binomial expansion. Geometry includes: the translation of Euclid's Elements of Geometry, the discussion of parallel axioms, and the calculation of pi (Kathy once calculated it to the decimal point 16). Triangulation is also more complete than ancient Greece and India.
From the12nd century, Arabic mathematics was gradually introduced to Spain and Europe through the cultural corridor west of the Mediterranean coast in North Africa. Especially decimal numbers, written calculations, translation of geometric elements, etc. It has had an important influence on the development of mathematics in western Europe and even the whole world. Some contents of China's ancient mathematics (decimal notation, proportion problem, indefinite equation, binomial expansion coefficient table, high-order open method, residual skills, etc.). ) were also introduced to Arabia (some of them were first introduced to India) and then introduced to Europe through Arabic mathematics.