Analysis of Applied Geometry in the Plan of Three Buildings Abubakr Taybadi, Goharshad Mosque and School of Ghiasieh Khargerd

The architect of Timurid have four systems or sets of proportions that could have combined them, but in general, a system had a major role. These systems can easily be equated to musical steps that although they are run by geometric progression, they are repeated. Each system is set based on an integer, but it is balanced by the root of that integer, according to geometric principles. Integers 2, 3, and 5 are each associated with geometric shapes determining the other elements of the scale. It was indeed Farabi who could discover the kinship of architecture with music, and then it was discussed by Bolatov. The nature of this system is well illustrated according to Farabi stating that the side of square and sector of circle in architecture is used as measuring instruments, and is similar to the theorem in logic and refrain in poetry, as well as poetry rhythms. It is precisely because of such an issue that Bolatov’s view can be accepted. Accordingly, the geometry of the design is not comparable with Western imaginations of proportion, which deals with the repetition of similar or related forms. In addition to its practical value, as an implementation procedure, the Islamic system provided the coordination and harmony for all parts, thereby the entire parts were associated with a single nature, like the relation of the parts of squares, triangles and pentagons with each other.