Volume 11, Issue 1 (Semi-Annual 2026)
CIAUJ 2026, 11(1): 183-206 |
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Naseri H, Mahmoudi Kamelabad M, De Angelis E. (2026). Geometric Thinking as a Cognitive Framework in Architectural Design: Conceptualizing Key Attributes Based on Grounded Theory and Expert Perspectives. , CIAUJ. 11(1), 183-206. doi:10.66224/ciauj.11.1.687
URL: http://ciauj-tabriziau.ir/article-1-687-en.html
URL: http://ciauj-tabriziau.ir/article-1-687-en.html
1- Department of Architecture, Faculty of Architecture and Urban Design, Art University of Isfahan, Isfahan, Iran
2- Department of Architecture, Faculty of Architecture and Urban Design, Art University of Isfahan, Isfahan, Iran ,m.mahmoudi@aui.ac.ir
3- Department of Architecture, Built Environment and Construction Engineering, Politecnico di Milano, Milan, Italy
2- Department of Architecture, Faculty of Architecture and Urban Design, Art University of Isfahan, Isfahan, Iran ,
3- Department of Architecture, Built Environment and Construction Engineering, Politecnico di Milano, Milan, Italy
Abstract: (1718 Views)
In architecture, design emerges from complex cognitive processes that integrate perception, imagination, reasoning, and decision-making. Among the various forms of knowledge influencing architectural thinking, geometry occupies a central position. It functions not only as a technical tool for measurement, drawing, and construction but also as a conceptual framework through which ideas are transformed into coherent spatial and formal structures. Mastery of geometric knowledge enables architects to organize space, establish proportions, and generate architectural forms with clarity and intelligibility. This study aims to identify and conceptualize geometric thinking in architectural design and to develop a grounded model explaining its role in enhancing architects’ cognitive skills. A qualitative research approach based on grounded theory was employed, using a purposive review of theoretical texts and scholarly works related to architecture, geometry, and thinking. Data collection and analysis were conducted simultaneously through open, axial, and selective coding using MAXQDA software, continuing until theoretical saturation was achieved. The findings indicate that geometric thinking is shaped by interrelated causal, contextual, and intervening factors. Causal factors include the rigor of geometric reasoning and the recognition of geometry as a foundational system of architectural knowledge. Contextual factors involve the distinction between sensory and intellectual geometry, as well as theoretical and practical dimensions. Intervening factors encompass measures, proportions, and rules that regulate order and harmony in architectural space. The identified strategies—such as valuing geometric principles through logical reasoning and discovering geometric rules through systematic analysis—enable structured and rational approaches to design, leading to improved understanding, precision, and mental clarity in the design process. In conclusion, the proposed conceptual model highlights the cognitive, epistemological, and practical significance of geometry in architectural design. Cultivating geometric thinking enhances design coherence, quality, and rationality, offering valuable insights for both architectural education and professional practice.
Keywords: Design Epistemology, Design thinking, Geometric Reasoning in Architecture, Grounded theory, Spatial Cognition
Type of Study: Original Article |
Subject:
Conceptualization of theorizing in Islamic architecture and urban ism
Received: 2025/12/22 | Accepted: 2026/04/28 | ePublished: 2026/06/28
Received: 2025/12/22 | Accepted: 2026/04/28 | ePublished: 2026/06/28
References
1. Aalamzadeh, A. A. (1999). Fundamentals of geometry. Elmi va Fanni [in Persian].
2. Abbasi, N., Ghasemi Sichani, M., Valibeig, N., & Saedavandi, M. (2019). Evaluation of the viewpoints of muslim mathematicians (2-11 Centuries AH) about the concept of geometry in architecture. Andisheh-ye Me'mari, 3(5), 84-105 [in Persian]. [DOI:10.30479/at.2019.10296.1141]
3. Abolghasemi, L. The Norm of Formation in Islamic Architecture of Iran. Tehran: Samt, 2006 [in Persian].
4. Al-Bīrūnī, A. R. Muḥammad ibn Aḥmad. (1973). Al-Tafhīm li-awāʾil ṣināʿat al-tanjīm (J. Homāyī, Ed.). Anjoman-e Asar-e Melli [in Persian].
5. Al-Safa, A. (1957). The Treatises of Ikhwan Al-Safa and Khalan Al-Wafa. Beirut: Aldar-Islamiah.
6. Al-Sayed, K., Dalton, R. C., & Hölscher, C. (2010). Discursive design thinking: The role of explicit knowledge in creative architectural design reasoning. AI EDAM, 24(2), 211-230. [DOI:10.1017/S0890060410000065]
7. Anderson, J. R. (1995). Cognitive psychology and its implications. Macmillan.
8. Antoniades, A. C. (2010). Poetics of architecture (Vol. 2; A. Ay, Trans.). Soroush Publications [in Persian].
9. Avani, Shahin. (2017). Ravesh-e Dekarti: Riyāzi yā hendesi? Falsafeh va Elāhiyāt, 22(3), 129-156 [in Persian].
10. Balkhārī Qahī, H. (2016). Philosophy of geometry and architecture. University of Tehran Press [in Persian].
11. Bolden, G. (2006). Creative thinking (S. A. Mirzaei, Trans.). Sargol [in Persian].
12. Caldwell, B., Dake, D., Safly, M., & Ulch, L. (2004). Integrated Hots Thinking Model. Ames, IA: Department of Art and Design, Iowa State University.
13. Cross, N. (2011). Design thinking: Understanding how designers think and work. Berg. [DOI:10.5040/9781474293884]
14. Dahar, A., & Alipour, R. (2013). Geometric analysis of Sheikh Lotfollah Mosque architecture to determine the geometric relationship between the prayer hall and entrance forecourt. Bagh-e Nazar, 10(26), 33-40 [in Persian].
15. Dehkhoda, A. A. (1998). Dehkhoda dictionary (Digital edition). Dehkhoda Dictionary Institute, University of Tehran [in Persian].
16. Donato, S. (1990). Iran: la ricostruzione delle aree distrutte dalla guerra: dalla politica dell'emergenza alla pianificazione culturale del recupero e della riqualificazione urbana. (No Title).
17. Edwards, B. (1992). Drawing on the Right Side of the Brain. In CHI'97 Extended Abstracts on Human Factors in Computing Systems (pp. 188-189). [DOI:10.1145/1120212.1120336]
18. Eram, S. (2021). The application of geometric thinking in mathematics (Master's thesis). Shahid Chamran University of Ahvaz [in Persian].
19. Fakouri Hajiar, H., Naderi, E., Shari'atmadari, A., & Seif-Naraghi, M. (2007). Content analysis of elementary science textbooks based on thinking foundations. Educational Research, 3(12), 97-122 [in Persian].
20. Farabi, A. N. (2003). What should be learned before philosophy (H. Mirrokni, Trans.). Fallat [in Persian].
21. Farasatkhah, M. (2009). Evaluation of the quality of higher education in Iran: An application of grounded theory. Institute for Research and Planning in Higher Education [in Persian].
22. Feizi, M., & Khakzand, M. (2005). Design thinking in the architectural design process. Bagh-e Nazar, 2(4), 13-23 [in Persian].
23. Feizollah Beigi, A., Golabchi, M., & RezaZadeh Ardebili, M. (2019). Analysis of theoretical and practical geometry of Abbasi jame Mosque's discontinuous double shell dome. Honarhaye Ziba: Architecture and Urbanism, 24(4), 35-48 [in Persian]. [DOI:10.22059/jfaup.2020.279322.672253]
24. Fisher, R. (2006). Teaching thinking to children (M. Safaei Moghaddam & A. Najarian, Trans.). Reshesh [in Persian].
25. Ghasemi-Far, N. (2004). Mechanisms of thinking. Qasideh Sara [in Persian].
26. Ghonim, M. (2016). Design thinking in architecture education: issues, limitations, and suggestions. In Proceedings of the 3rd International Architectural Design Conference on Design and Nature ARCHDESIGN (Vol. 16, pp. 553-561). Istanbul: Dakam Publishing.
27. Gilhooly, K. J. (1996). Thinking: Directed, undirected and creative. Academic Press.
28. Goldschmidt, G. (2014). Linkography: Unfolding the design process. MIT Press. [DOI:10.7551/mitpress/9455.001.0001]
29. Gorji Mahlabani, Y. (2007). Design thinking and its process patterns. Soffeh, 16(2), 106-123 [in Persian].
30. Guthrie, W. K. C. (1996). A history of Greek philosophy: Pythagoras and the Pythagoreans (M. Ghavam Safari, Trans.). Fekr-e Rooz [in Persian].
31. Ibn ʿArabī, M. al-D. M. ibn ʿAlī. (2007). Fuṣūṣ al-ḥikam (M. A. Movahhed Abtahi & S. Movahhed, Trans.). Karnameh.
32. Javadi Nodeh, M., Shahcheraghi, A., & Andalib, A. (2022). An Investigation of the Golden Proportions and Geometric Principles Derived from Nature in the Structural Components of the Traditional Houses (Case Study: Qajar Houses in Ardabil). Bagh-e Nazar, 19(110), 35-48 [in Persian]. [DOI:10.22034/bagh.2022.295674.4973]
33. Josephine, E. E. C. (2017). The study of geometric forms, proportion and scale of heritage buildings due to architectural theory. IPTEK Journal of Proceedings Series 3(3): 263-272. [DOI:10.12962/j23546026.y2017i3.2455]
34. Karvan, F. (2021). Design process from idea to presentation based on reflective thinking and learning styles in architecture students. Soffeh, 31(2), 23-38 [in Persian]. [DOI:10.52547/sofeh.31.2.23]
35. Karvan, F. (2023). Developing a design thinking model of architectural education based on wisdom and creativity styles mediated with self-directed learning. Armanshahr, 54(44), 111-124 [in Persian]. http://doi.org/10.22034/AAUD.2023.344408.2675
36. Kotnik, T. (2010). Algorithmic architecture: Computational design thinking. Architectural Design, 80(2), 52-59. [DOI:10.1002/ad.1063]
37. Lawson, B. (2006). How designers think (4th ed.). Elsevier. [DOI:10.4324/9780080454979]
38. Lawson, B. (2013). How designers think: Demystifying the design process (H. Nadimi, Trans.). Shahid Beheshti University Press [in Persian].
39. Lipman, M. (2004). Philosophy and children (Interview with Saeed Naji). Ketab-e Mah-e Adabiat va Falsafeh, 75-76, 26-31 [in Persian].
40. Mahmoodabadi, A., & Mirjany, H. (2022). The ratio of architectural design thinking to incompatible schemas. Andisheh-ye Me'mari, 6(12), 1-16 [in Persian]. [DOI:10.30479/at.2022.16531.1830]
41. Mahmoudi, A. S. (2004). Thinking in design: Introducing an interactive thinking model in design education. Honarhaye Ziba, (20), 27-36 [in Persian].
42. Masahheb, G. H. (2004). Persian encyclopedia. Amir Kabir [in Persian].
43. Mehdian, M., Liaqatdar, M. J., & Arizi, H. R. (2017). Model for Geometric growth thinking: the impact of visual memory on the Geometric thinking through Geometrey scientific epistemology. Journal of Educational Sciences, 24(1), 45-69 [in Persian]. [DOI:10.22055/edu.2017.17661.1784]
44. Mehdizadeh Seraj, F., Tehrani, F., & Valibeyg, N. (2012). Applying the Hanjar Triangles in the Mathematical Calculation, Implementation and Enforcement of Traditional Iranian Architecture. Iranian Restoration and Architecture, 1(1), 15-26 [in Persian]. https://dor.isc.ac/dor/20.1001.1.23453850.1390.1.1.1.9
45. Menges, A., & Ahlquist, S. (2011). Computational design thinking: computation design thinking. John Wiley & Sons.
46. Minkovskaya, E. L. (2000). Toward the study of architectural forms in Central Asia at the end of the 14th century (Mausoleum of Khoja Ahmad Yasavi). Asar, 30-31, 260-288 [in Persian]. http://journal.richt.ir/athar/article-1-193-fa.html
47. Molavi, B. (2002). A study of the application of geometry in Iran's past architecture. Ministry of Housing and Urban Development [in Persian].
48. Mozaffar, F., & Kianersi, M. (2019). The Main Factors of Promoting Designerly Thinking (Conventional and Situation-based Thinking) in Teaching the Basics of Architectural Designing. Iranian Restoration and Architecture, 9(18), 1-18 [in Persian]. https://dor.isc.ac/dor/20.1001.1.23453850.1398.9.18.2.0
49. Nabavi, F. and Y. Ahmad. (2016). Is there any geometrical golden ratio in traditional Iranian courtyard houses? ArchNet-IJAR: International Journal of Architectural Research 10(1): 143-154. 10.26687/archnet-ijar.v10i1.744?urlappend=%3Futm_source%3Dresearchgate.net%26utm_medium%3Darticle
10.26687/archnet-ijar.v10i1.744 []
50. Nadimi, H. (1999). The truth of ornament. Farhangestan-e Olum, (14-15), 19-34 [in Persian].
51. Najiboglu, G. (2000). Geometry and ornament in Islamic architecture (M. Ghiomi Bidhendi, Trans.). Rowzaneh [in Persian].
52. Nasr, S. H. (2000). The need for a sacred science. Tahā Cultural Institute [in Persian].
53. Nejad Ebrahimi, A., & Tooranpoor, M. (2021). Investigating Geometry used in Khargerd Ghiasiyyah School with Emphasis on Practical Geometry of Abolafa Bozjani. Nameh-ye Architecture and Urbanism, 13(31), 101-116 [in Persian]. [DOI:10.30480/aup.2021.2627.1517]
54. Nejad Ebrahimi, A., & Ya'ghoubloo, M. (2019). An introduction to theoretical geometry in architecture. Research in Art and Humanities, 4(5), 19-34 [in Persian].
55. Nejad Ebrahimi, A., Gharabaghlou, M., & Farshchian, A. (2021). The status of theoretical wisdom in architectural geometry by Islamic mathematicians. Contemporary Wisdom, 12(1), 271-305 [in Persian].
56. Neyestani, J. (2005). History of map drawing and the application of geometry and arithmetic in Islamic architecture. Peyk-e Noor, 3(5), 42-49 [in Persian].
57. Noori Mokaram, A., Janipour, B., & Taghvaei, V. (2023). Examining the Components of Architectural Concept Formationin Teaching Architectural Design With A Background-Based Approach. Bagh-e Nazar, 20(120), 29-42 [in Persian]. [DOI:10.22034/bagh.2022.332886.5186]
58. Nouhi Bezanjani, M., & Ghasemi, M. (2020). Analysis of the concept of geometry in traditional Iranian architecture and its application in contemporary architecture. Architectural Studies, 3(17), 165-175 [in Persian].
59. Omoumi, M. (1997). Architecture, pattern, and order. Khak [in Persian].
60. Oxman, R. (2004). Think-maps: Teaching design thinking in design education. Design Studies, 25(1), 63-91.
https://doi.org/10.1016/S0142-694X(03)00033-4 [DOI:10.1016/S0142-694X(03)00036-2]
61. Pope, A. U., & Ackerman, P. (1999). A survey of Persian art (N. Daryabandari, Trans.). Scientific and Cultural Publications [in Persian].
62. Rosenfeld, B. (1979). Ghiyath al-Din Jamshid Kashani (P. Shahriari, Trans.). Elmi va Farhangi [in Persian].
63. Saliba, J. (1991). Dictionary of philosophy and social sciences (K. Bargnisi & S. Sajjadi, Trans.). Modiran [in Persian].
64. Seif, A. A. (2017). Modern educational psychology: Psychology of learning and instruction. Doran [in Persian].
65. Seyyed Sadr, S. A. (2002). Encyclopedia of architecture and urbanism. Azadeh [in Persian].
66. Shabani, H. (1993). Educational and training skills. SAMT [in Persian].
67. Sharif, H. R. (2009). Architectural design process and critical thinking (Doctoral dissertation). Shahid Beheshti University [in Persian].
68. Sharif, H. R. (2011). Critical thinking and evaluation of architectural design ideas. Soffeh, 21(2), 53-64 [in Persian].
69. Shoari-Nejad, A. A. (1991). Logical thinking. SAMT [in Persian].
70. Silvayeh, S., Daneshjoo, K., & Farmahin Farahani, S. (2013). Geometry in pre-Islamic Iranian architecture and its manifestation in contemporary Iranian architecture. Naqsh-e Jahan, 3(1), 55-66 [in Persian]. https://dor.isc.ac/dor/20.1001.1.23224991.1392.3.1.3.0
71. Solso, R. (2009). Cognitive psychology. Roshd Publications [in Persian].
72. Sternberg, R. J. (1997). Thinking styles. Cambridge university press. [DOI:10.1017/CBO9780511584152]
73. Tayah, S., Mehdizadeh Seraj, F., & Mahmoudi Zarandi, M. (2020). Revisiting Nature-inspired Thinking Process in Architectural Designs Using Zaltman's Metaphor Method (ZMET). Bagh-e Nazar, 17(91), 65-80 [in Persian]. [DOI:10.22034/bagh.2020.218157.4449]
74. Valibeig, N., Nasekhian, S., & Nazariyeh, N. (2017). An Analysis of the Impact of Shading Wall Geometry on Formation of the Ice Houses in Southeast of Iran (Case Study: Kerman). Nameh-ye Architecture and Urbanism, 9(18), 147-166 [in Persian]. [DOI:10.30480/aup.2017.517]
75. Vasiq, B., Naseri, H., & Bakhtiari, S. (2022). Investigating axis concepts in Yazd mosques. Urban Identity, 16(49), 5-16 [in Persian]. [DOI:10.30495/hoviatshahr.2022.53200.11960]
76. Whitley Eves, H. (2014). History of geometry (M. H. Shafieeha, Trans.). Elmi va Farhangi [in Persian].
77. Yaftian, N., & Safabakhsh Chekousari, A. (2019). Teaching and learning geometry: Introducing the Van Hiele theory. Mathematics and Society, 4(3), 9-22 [in Persian]. [DOI:10.22108/msci.2020.118021.1329]
78. Zandieh Vakili, M. (2018). Feasibility of applying geometry used in Islamic architectural experiences to contemporary Iranian architecture toward form-structure interaction (Doctoral dissertation). University of Art, Isfahan [in Persian].
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