History of Geometry - Islamic Geometry

Islamic Geometry

The Islamic Caliphate established across the Middle East, North Africa, Spain, Portugal, Persia and parts of Persia, began around 640 CE. Islamic mathematics during this period was primarily algebraic rather than geometric, though there were important works on geometry. Scholarship in Europe declined and eventually the Hellenistic works of antiquity were lost to them, and survived only in the Islamic centers of learning.

Although the Muslim mathematicians are most famed for their work on algebra, number theory and number systems, they also made considerable contributions to geometry, trigonometry and mathematical astronomy, and were responsible for the development of algebraic geometry. Geometrical magnitudes were treated as "algebraic objects" by most Muslim mathematicians however.

The successors of Muḥammad ibn Mūsā al-Ḵwārizmī who was Persian Scholar, mathematician and Astronomer who invented the Algorithm in Mathematics which is the base for Computer Science (born 780) undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose.

Al-Mahani (born 820) conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Al-Karaji (born 953) completely freed algebra from geometrical operations and replaced them with the arithmetical type of operations which are at the core of algebra today.