Journal of Iranian Architecture & Urbanism(JIAU)

Abstract Extended Abstract
Background and Objectives: The existence of numerous examples of the connection between the knowledge of geometry and building design, with an emphasis on the application of geometry in architecture, especially in the Islamic era, introduces architecture as a knowledge-based skill that creates an extended connection between thought and action. The breadth of this connection has created numerous definitions of the concept of geometry and its diverse applications in architecture. Due to the importance of paying attention to the internal aspects of phenomena in the formation and advancement of sciences in the Islamic worldview, it is essential to understand the concept of geometry in architecture. With the aim of providing a single definition of the concept of the word geometry for the emergence and manifestation of its capabilities in architecture, the first research question, “What is the meaning of the word geometry and its application in architecture?”, is formed on the assumption that the numerous existing interpretations of the concept of the word geometry create diverse applications of geometry in architecture. Considering that the theoretical and practical topics of geometry were taught to architects in the past by Muslim philosophers and mathematicians, and today, architects are trained in architectural schools, with the aim of compiling the necessary syllabus for teaching the clarified subject of geometry to architects, the second research question, “How does the concept of the word geometry in architecture affect its educational content?”, is formed on the assumption that introducing the subject of geometry to architects based on its clarified concept in this research, reveals the need to compile educational syllabuses that cover various areas of the aforementioned concept.
Methods: This research is conducted using a descriptive-analytical method and with the help of qualitative content analysis. Data are collected through library studies and by deductive method. In order to enter the field of research, Often from Islamic sources, well-referenced scientific articles and authentic books have been selected that are related to the subject and whose authors are experts in the field under investigation. In order to answer the first question, with the help of logical reasoning, we will deal with the epistemological classification and content matching of existing definitions of the concept of the word geometry with existing interpretations of it in architecture. Then, the applications resulting from the aforementioned interpretations are introduced using inference argument. In order to answer the second question, with the help of logical reasoning and considering the clarified subject of geometry, we adapt the syllabus and objectives of basic and optional courses related to geometry education in architecture in terms of content with the theories of Muslim scholars from the fourth to the eleventh centuries AH. Then, using inference argument, the materials needed for teaching are discovered.
Findings: According to studies, the word “Geometry” is defined as equivalent to the word “Qadar” in the sense of (certain size) which is understood in the three realms of measurement, proportion, and exaltation to the higher worlds. Also, the numerous existing interpretations of the concept of geometry in architecture fall into the categories of: ordering, coordinating, and metaphorical, respectively and in accordance with the sub interpretations, applications are introduced under the title of “Geometric-Architectural Layout”. In short, the concept of the word “Geometry” in architecture is an art that has come down from the Supreme World in shapes and sizes in order to fulfill the goals of the building built and the manifestation of the divine names and it has three levels: drawing plane, spatial and analytical-content. In order to benefit from all the aforementioned levels and to achieve the “Secret of Qadar” of the building, an application called “Unifying Geometrical-Architectural Layout” is proposed. It should be noted that just as the aforementioned layouts are different in nature, the educational and research strategies of geometry in architecture are also different from each other. In the educational model proposed by Muslim philosophers, geometry is a tool for realizing Islamic life, in which the concept of “Kail” is used to promote and improve the relationship between man and the environment.
Conclusion: Using inference argument, we find out that knowing the concept of the word “Geometry” in an incomplete form due to its wide scope, has become the basis for the existence of many interpretations and, as a result, the numerous applications of the concept of geometry in architecture. In fact, each architect uses a part of the concept of geometry in architecture according to her needs and thus numerous geometric-architectural Layouts are formed and the first hypothesis of the research is confirmed. Next, while matching the content of the levels of the concept of the word “Geometry” in architecture with the content resulting from summarizing the components of the theories of Muslim philosophers and the selected goals and headings appropriate to these goals, using logical reasoning, we compile syllabuses for teaching the clarified subject of geometry in architecture, and we also classify them according to the content of educational and research approaches: exploratory-descriptive, analytical-interpretive and causal and thus the second hypothesis of the research is also confirmed.

Abstract Extended Abstract
Background and Objectives: Throughout the history of human thought, numerous theories have emerged concerning the essence of architecture, its fundamental components, and the role and significance of each element. These theoretical perspectives have profoundly influenced how architecture is conceptualized, practiced, and taught. Dominant paradigms such as formalism and strict functionalism, for example, often reduce architecture to a purely visual or utilitarian construct—one that functions merely as a physical container for human activity. Such reductionist views tend to overlook the fixed and multidimensional nature of human beings, whose needs extend beyond the material to encompass emotional, sensory, intellectual, and spiritual dimensions. As a result, these perspectives fall short of addressing the full richness of human experience and hinder architecture’s potential to contribute to human flourishing. Among the elements that have been neglected or insufficiently explored in many of these modern approaches is the concept of “geometry.” Far more than a technical or decorative tool, geometry has historically served as a foundational and generative principle in architecture—one that organizes space, creates harmony, and reflects deeper metaphysical realities. This research seeks to re-examine the role of geometry within the broader system of creation, and by extension, within architectural design, through the lens of Islamic philosophy and thought. By adopting this holistic and spiritually grounded framework, the study aims to uncover the true ontological and functional status of geometry in architecture. Ultimately, it aspires to contribute to a richer pedagogical and practical approach to architectural education and design—one that is aligned with the innate nature of human beings and supports a more meaningful, purposeful built environment.
Methods: Initially, the research examines the definition and position of geometry across various human schools of thought. Using an interpretive-analytical approach and authentic Islamic sources, the study identifies this concept and its place within the system of existence, including architecture, thereby shaping the theoretical framework of the research. Through logical reasoning, the roles of geometry in architecture are extracted from this theoretical framework. For a comprehensive understanding, the four causes of geometry in architecture are identified and examined through a case study of the “House of Kaaba,” a manifestation of divine architecture.
Findings: The indicate the following:
- Efficient Cause: Geometry organizes architectural elements into a unified whole for human use, aiming for the perfection of human life.
- Final Cause: Geometry conveys meaning aligned with the architectural function, guiding individuals towards worship and understanding.
- Material Cause: The element of “space,” which must possess specific characteristics and features in each building, proportional to its function and human perceptual powers.
- Formal Cause: The limiting and distinguishing aspects of space (such as floors, ceilings, and exteriors), which must be proportionate to the building’s function and intended meaning, leading to the creation of a unique internal and external volume, decorated with appropriate arrangements.
Conclusion: This research underscores the profound significance of geometry in the realm of architecture, particularly through the lens of Islamic thought. By exploring the theoretical foundations and practical applications of geometry, the study reveals its essential role as the primary generator and organizer of architectural elements. The identification of the four causes—efficient, final, material, and formal—provides a comprehensive understanding of how geometry shapes and enhances architectural design. The case study of the Kaaba exemplifies the divine and functional aspects of geometry, demonstrating its capacity to harmonize architectural elements, convey meaningful symbolism, and create spaces that cater to both human perceptual powers and spiritual needs. This holistic approach not only enriches the sensory and spiritual dimensions of human life but also offers a robust framework for contemporary architectural practice. Ultimately, this research advocates for a renewed emphasis on geometry in architectural education and design, promoting a more integrated and meaningful approach that aligns with the holistic nature of human existence.

Abstract Extended Abstract
Background and Objectives: The history of Iranian-Islamic architecture is filled with remarkable and magnificent works created by artists who utilized geometric knowledge and principles. Geometry served as a common language among architects in designing these structures. With advancements in technology and new geometric knowledge, innovative design methods have emerged. Parametric architecture is one of the approaches that enables the exploration of relationships between masses and complex shapes within computer environments. Experts suggest that these architectural works stem from the application of parametric design thinking throughout the planning and design processes. However, examining these principles within architectural knowledge is challenging due to the diversity across various fields, including functional and structural and other aspects. This research focuses on this process as it pertains to temporary residences, such as caravanserais.
Methods: This research relies on bibliographic studies and computational methods to identify the geometric and mathematical principles used in the design of notable suburban caravanserais. The data are analyzed using reliable software that algorithmizes and simulates parametric problems, visually displaying results to support the hypothesis.
Findings: The findings indicate that artists skillfully controlled and recreated design principles according to the existing criteria and conditions of their time, resulting in remarkable works that fulfilled contemporary needs. The design process explored in this study is confined to producing square or rectangular plans, though this constraint can be adjusted by parameterizing the initial information to generate polygonal plans such as hexagons or octagons. This approach also elucidates several hexagonal and octagonal designs in Iranian-Islamic caravanserais, which closely resemble quadrilateral plans in spatial organization. A notable characteristic of Islamic architecture is its multi-functionality; Iranian-Islamic architecture produced “complete building forms” adaptable for various purposes. A single building plan might serve for both fortresses and caravanserais, often making it difficult to differentiate them by plan alone. Thus, the parametric framework established in this project can apply not only to caravanserai buildings but also to desert castles, palaces, and schools with similar designs. It is important to note that the diversity of Islamic architectural types means that the parametric order developed here does not claim to encompass all caravanserais. Rather, it offers a design approach rooted in Iranian-Islamic principles, analyzed through Grasshopper software using three case studies.
Conclusion: Parametric design is a design paradigm where the relationships between elements dictate the reproduction of geometry and complex forms, allowing the outcome of a system or equation to be modified by adjusting specific parameters and variables. The results indicate that this rule-based methodology aligns with the geometric design production techniques of Iranian-Islamic architecture. By introducing constituent parameters and employing algorithmization in Grasshopper software, the parameterization of the overall plans for four-balcony out-of-town caravanserais is validated. This conclusion can extend to caravanserai plans and similar building functions, such as schools, in other architectural styles, including double-sided and polygonal designs. Furthermore, the significant advancements in architectural technology allow designers to leverage the rich knowledge of historical architecture using contemporary programming languages. Consequently, applying parametric architecture principles and tools like Grasshopper enables programming based on crucial parameters that influence the creation and development of valuable architectural works. The principles and rules governing algorithm creation are derived from the knowledge of Iranian-Islamic architectural design, allowing for the development of algorithms in parametric language through the analysis of caravanserai plans.