rvived to modern times began with this tradition. It was continued in the Islamic world, where original developments based on these masterpieces first appeared. Islamic and Indian Mathematics After a century of expansion in which the religion of Islam spread from its beginnings in the Arabian Peninsula to dominate an area extending from Spain to the borders of China, Muslims began to acquire the results of the “foreign sciences.” At centers such as the House of Wisdom in Baghdad, supported by the ruling caliphs and wealthy individuals, translators produced Arabic versions of Greek and Indian mathematical works. By the year 900 AD the acquisition was complete, and Muslim scholars began to build on what they had acquired. Thus mathematicians extended the Hindu decimal positional system of arithmetic from whole numbers to include decimal fractions, and the 12th-century Persian mathematician Omar Khayyam generalized Hindu methods for extracting square and cube roots to include fourth, fifth, and higher roots. In algebra, al-Karaji completed the algebra of polynomials of Muhammad al-Khwarizmi. Al-Karaji included polynomials with an infinite number of terms. (Al-Khwarizmi's name, incidentally, is the source of the word algorithm, and the title of one of his books is the source of the word algebra.) Geometers such as Ibrahim ibn Sinan continued Archimedes' investigations of areas and volumes, and Kamal al-Din and others applied the theory of conic sections to solve optical problems. Using the Hindu sine function and Menelaus's theorem, mathematicians from Habas al-Hasib to Nasir ad-Din at-Tusi created the mathematical disciplines of plane and spherical trigonometry. These did not become mathematical disciplines in the West, however, until the publication of De Triangulis Omnimodibus by the German astronomer Regiomontanus. Finally, a number of Muslim mathematicians made important discoveries in the theory of numbers, while others ex...
