Studying Muqarnas Typology and Its Fundamental Components according to Al-Kāshi’s Meftāh-ol- Hessāb Treatise

Muqarnas, also called “honeycomb vaulting” or “stalactite vaulting”, is usually considered the key component and the primary characteristic of Islamic architecture. The aim out of applying muqarnas is to create a smooth, decorative transition zone in an otherwise bare structural space. This decorative architectural element has been used within a variety of architectural settings from its beginning. Having thousands of complex geometric patterns composed of several combinations of simple elements makes muqarnas one of the most elaborate and fascinating forms of architectural ornaments. From a long time ago, that characteristic has attracted several scholars and researchers from different parts of the world to study and analyze muqarnas structures and patterns. Although there are several researches expressing opinions on the classification of muqarnas types, the issue is still under debate. Interestingly, one of the most adopted muqarnas typology studies dates back to a 15th century in a treatise written by an Iranian famous scholar, Qiyāth-od-Din Jamshid Mas’ud al- Kāshāni (1380-1429) mostly known as al-Kāshi in west. This book is Al- Kashi’s most impressive mathematical work called Meftāh-ol-Hessāb (The Key to Arithmetic) which he completed on March 1427, two years before his death. The work is a major text intended to be used in teaching the necessary mathematics to those studying astronomy, surveying, architecture, accounting and trading. In the fourth essay of the book, the first available written text on muqarnas mathematical and geometrical studies has been presented. While this essay was written to teach how to calculate muqarnas surfaces, it presents a typology for muqarnas and also introduces the main structural components and units of muqarnas for the first time. Astonishingly, after more than 590 years there are still diverse interpretations on the types as well as the fundamental units of muqarnas according to his points of view. While it is mostly due to the complicated writing style of Al-Kashi in Arabic, another main reason is that you can hardly find any 3D analysis of Al-Kashi’s studies. In fact, most researches have gone through the 2D patterns. Accordingly, this research tries to present a more accurate understanding of Al-Kashi’s treatise using 3D techniques. To do so, in the first phase the original essay in Arabic has been studied with the help of the Arabic language scholars at Shiraz University in order to have a better comprehension of the text. Secondly, the related literature has been studied and compared. These phases help us understand that the key point in misunderstanding and/or different interpretations of Kashi’s muqarnas types lies in different understanding of muqarnas fundamental units as were described by Al-Kashi. In this regard, by carefully scrutinizing the Arabic text and studying the 2D and 3D patterns and details of the remained muqarnases from Al-Kashi era, muqarnas fundamental units/components are identified and presented in 3D schematic diagrams for the first time. This paper is introducing the components as followed: “outer shell”, “inner shell”, “lower roof”, “upper roof”, “facet” and “facet base”. This would help prevent the inaccurate use of technical vocabulary for identification of muqarnas structures and also result in more a accurate and concise understanding of Al-Kashi’s muqarnas typology. Using the introduced muqarnas components in the previous phase, in the last section a detailed identification of Al-Kashi’s muqarnas typology has been presented. In his essay, Al-Kashi classified muqarnas into four main categories, namely sādeh (simple), motayyan (clay-plastered), Qows (curved) and Shirazi. To draw a conclusion, this paper elaborates on the earlier research and explains how the first three types differ from each other in spite of being formed in a similar square and/or rhombic grid. It also depicts how Shirazi muqarnases are formed within a radial system, not following a specific module. They have more complex structures due to the variety of fundamental components used. Finally, the present paper concludes that although Al-Kashi’s typology was basically conducted for the specific purpose of calculating muqarnas surfaces besides surveying them and although his research has been limited to his own time samples, the muqarnas fundamental units and typology he introduced can still be used even now in order to have a better understanding of this architectural element and its structures.