Geometry came to the Islamic empire through the translation of Greek works,with most of geometry knowledge taken from the book of Euclid, Foundations of Geometry.Though scholarly works like Euclid, Apollonius and Archimedes were appreciated, Arab and Islamic scholars refuted their conclusions as well as correcting them. They also contributed to the field of theoretical geometry. Although it is a field not very much studied in depth much by Muslims.
Types of Geometry Developed by the Muslims
There are two types of Geometry the Muslims took from the Greek and developed and improved – Mental and Concrete Geometry. Mental Geometry refers to the Theoretical Geometry, where the Muslim scientists had only commented and do explanations. There were more concerned with the Concrete Geometry where they apply in industries, art and construction.
Development of Geometry under the Muslims
Geometry was developed by Muslim scientists during the Islamic civilization. In some publications of Al-Biruni, there are some geometrical theories, givens and proofs. These methods were unique from those of the Greek. Muslim scientists, including Ibn Al-Haytham, employed both plane and solid geometry to specify the reflection for statuses of spherical, cylindrical, conical, convex and concavo-convex, and they unprecedentedly introduced creative general solutions to them. Muslim scientists pointed out that how to identify the proportion of the periphery of the circle to its diameter. They also proved excellent in plane geometry concerning parallels. Nasir Al-Din Al-Tusi was the first one to draw the attention to prove that Euclid’s theory lacks the issue of parallels; he introduced evidence based on hypotheses in his book Al-Resala Al-Shfia An Alshk Fil Khotot Al-Mtwazia (Adequate Treatise on Doubts about Parallel Lines). Muslim mathematicians know how the science of flattening the circle. Haji Khalifa viewed this science as the “science through which we know how the circle is transferred to a surface by keeping lines and circles drawn on the circle and how these drawn circles are transferred to a circle then to a line. ” The importance of this science, according to Al-Qongy, lies in the fact that it can be used in other sciences, especially astronomy. Of their publications in this field of geometry are Al-Kamel by Farghani, Al-Isti’ab by Al-Biruni, and Dostour Al-Targih fi Kawaad Al- Tastih by –Taqi al-Din al-Shami.
Muslim scientists introduced a lot of publications on geometric problems, geometric synthesis, angle divisions, drawing of regular rectangular shapes, and linking them to algebric equations. It is said that Thabit ibn Qurra divided the angle into three equal sections using a way which was different from that known by Greeks.
Qadri Toqan pointed out that sines were used instead of hypotenuse at the beginning of the third hijjri century. It is said that it was Thabit ibn Qurra who introduced (Manalos claims), with their present form. Above all, he solved some of the cubic equations in geometrical ways sought by some western scientists in their mathematical research in the sixteenth century AD, including Cartan and other great mathematicians.
Qadri Toqan went on to say that those who are concerned with mathematics do not believe that Thabit was among those who paved the way for (calculus), a science which is of great significance for inventions and discoveries. But for all this science and its facilities for solving a lot of hard sums and operations, natural laws would not have been exploited for the benefit of humanity. Thabit was one of those concerned with analytic geometry and excelled in it. He introduced unprecedented innovations and wrote a book in which he explained the relation between algebra and geometry and how to combine them.
Another leap occurred in geometry when Al-Khwarizmi introduced algebra, which will be tackled when dealing with the contributions made by Muslims in human sciences.
In the field of area, the book, Marefet Mesahet Al-Ashkal Al-Basita Wa Al-Koreya (the Book of Measurement of the Plane and Spherical Figures) in geometry is considered one of the most important works of the Sons of Musa bin Shaker. In it, they emphasized the importance of identifying length, width and size.
This book by the Sons of Musa bin Shaker constituted a significant development of the two books of Archimedes on Measurement of a Circle and on the Sphere and Cylinder. In it, they utilized an approach used by udox and the concept of meager quantities introduced by Archimedes. This book was of great importance for the Islamic East and the Latinized west alike.
Muslim scientists tackled areas in their mathematical publications as being a branch of geometry. For example, Bahauldin Al-Aamili (1031 A.H./ 1622 A.D.) devoted the first three chapters of part six of his book Kholaset Al-Hesab( The Gist of Mathematics). In the introduction, he introduced basic definitions on area, especially the area of the surfaces and bodies. In chapter one, he dealt with the area of surfaces with straight sides as triangle, square, rectangle, rhombus, hexagon and octagon, among others. In chapters two and three, he focused on the way through which the area of circles, curved surfaces, such as cylinders, complete and incomplete cones and the circle. In part seven, he referred to some issues related to the area of the land surface to conduct surveying to dig canals and determine heights, width of rivers and depth of wells.
It was natural of Muslims to transfer their geometrical knowledge and apply it to their architectural art, depicted in masjids (mosques), places and cities, among others. They paid attention to geometrical decorations, which were characterized by symmetry and accuracy.
In view of the above, it is vivid clear that Muslims excelled in geometry; their role could not be ignored at all. Mohamed Kurd Ali pointed out that “As far as geometry is concerned, Muslims were peerless innovators. Arabs did not invent buildings of their own; their geometry was full of their love of decoration and nicety. They invented the propped arch and excelled in the geometry of domes, ceilings and suspended ceilings, made of trees and flowers for their mosques and palaces. All these decorations have rendered these places masterpieces. According to a foreign knowledgeable person, the excessive obsession of Muslims with decorations has made their buildings as an oriental dress, which was beautifully knit and ornamented.
These have been some of Muslim contributions to the development of geometry. The characteristics of this science became clear after they had checked the heritage of the previous civilizations.
Parts of the article is taken from http://en.islamstory.com/