A Comparison Between Quasiperiodic Order of Shah Gereh and the Quasicrystal Structure of Silicon

Geometry has always had high status in the world of tradition. Its status is emphasized even by the Islamic religious resources. According to some Islamic scholars, the notion of "Ghadr al-ma'loom" (the defined quantity) in the holy Quran refers to geometry and measurement. This testifies to the sacredness of mathematics, arithmetic, and geometry in Islamic worldview. Islamic scholars believe that the sacredness of mathematics and geometry appears nowhere more clearly than in art where the matter is dignified by geometry and arithmetic. In the Iranian Islamic architecture geometry played a prominent role, to the point that, scholars like Farabi in categorizing the sciences of their time, put architecture and mechanics under the category of practical geometry, while geometry itself was categorized as a branch of mathematics. Some scholars believe that in Iranian architecture especially in Timurid period geometry is not just a means to achieve a goal; rather it is a goal in itself. Geometry is a hidden meaning in this architecture and an aesthetic standard for that. This paper aims to explore, discover, and describe the geometrical structure of Gereh-work, and to compare its order with the order present in natural constructions. The descriptive method is utilized to do so. This research has this idea as its hypothesis that the reason why there is a noticeable similarity between some aspects of traditional architecture and some natural constructions is not a direct copying from nature, instead is the use of geometry and possessing remarkable mastery of the geometrical principles that are fundamental in creation of natural entities. In this research, first the relevant literature is reviewed. Here the history of Gereh, different types of Gerehs, and the methods for designing and drawing them are reviewed. Regarding their expansion methods two types of them are recognized: Gerehs with a periodic order and Gerehs with a quasi-periodic order. Then the geometrical order of the structure of alloy AL70.Ni15.Co15 is compared with that of a decagonal Gereh. After that, the quasi-periodic order of self-similar Gerehs (Shah Gerehs) is compared with that of quasi-crystals. To do that, the Shah Gereh of the western Iwan of Jame' mosque of Isfahan was used as a sample of self-similar Gerehs and the element of silicon was selected as a sample of quasi-crystals. This comparison illustrates an evident similarity between the two samples. According to the findings of this research the structure of this alloy can be overlaid with obtuse and acute Gerehs in three different scales. One of the primary findings of this research is that the intelligent use of geometry by the Muslim artisans has caused their art to resemble astonishingly to crystals and quasi-crystals which are believed to be the most accurate creatures of the material world. Furthermore, it becomes obvious that this similarity between Gerehs and microscopic structure of quasi-crystals is not brought about by direct copying from nature because the traditional architects were not able to observe these microscopic structures. Therefore, the vital role of geometry in traditional Islamic architecture is emphasized again.