مرکز منطقه ای اطلاع رسانی علوم و فناوری مطالعات شهر ایرانی-اسلامی 2228-639X 15 57 2025 7 12 Studying the Historical Evolution of the Basic Pattern in the Architecture of the Ancient Period and Iranian Tradition بررسی سیر تحولات تاریخی الگوی مبنا در معماری دوره باستان و سنت ایران 25 47 fa فرشاد حاتمی برق آزاد اسلامی واحد تهران-غرب بهروز منصوری آزاد اسلامی واحد تهران-مرکز سید مصطفی مختاباد امرئی دانشگاه تربیت مدرس تهران لیلا زارع آزاد اسلامی واحد تهران-غرب 2024 11 15  Studying the Historical Evolution of the Basic Pattern in the Architecture of the Ancient Period and Iranian Tradition   Farshad Hatami Bargh<a href="#_ftn1" name="_ftnref1">*</a>  Behrouz Mansouri<a href="#_ftn2" name="_ftnref2">**</a>  Sayyed Mostafa Mokhtabad Amrei<a href="#_ftn3" name="_ftnref3">**</a>  Leila Zare<a href="#_ftn4" name="_ftnref4">****</a>   The role and importance of the influence of geometry and mathematics in Iranian architecture since pre-Islamic times has been used in the form of technical (experimental) architecture and pattern (Mendel) as a practical application in the geometric arrangement of buildings. It has been observed in many buildings with sovereign, ceremonial-residential, and residential uses, respectively, of the social classes of the elite and the common people in ancient times and after Islam; the fourth to tenth centuries A.H., and the approach of influences in functional spaces and following early patterns in the Iranian architectural style is expressed as indoor and outdoor spatial functions. Studies of the course of historical developments show that residential architecture in Iran has resulted from the use of a formal pattern as a spatial arrangement in examples of buildings from three historical periods: ancient, traditional, and modern. In this research, data collection is library-based and the research method is interpretive-historical, descriptive-analytical. The aim of the research is to explain the impact of the developments of formal patterns in the form of architectural crafts, which is influenced by applied geometry and mathematics, which is reinforced by the studies of Iranian philosophers including Khwarizmi, Banu-musa, Abu al-WafaBuzjani, Ikhwan al-Safa, Nasir al-Din al-Tusi and Sheikh Bahai Also, since the beginning of the third century A.H., under the influence of mathematics and geometry discussions, following numbers and estimating distances, geometry in the form of the second dimension, the third dimension, and finally the architectural craft and mystical meanings and the journey and transcendence (rational-sensible) are reflected in the combination of the order of Platonic shapes and volumes in religious places. The results of the research show that the use of the basic pattern in residential buildings is influenced by the use of mathematics and geometry in Iranian formal and modular meanings, which had its initial origin in Chahar-Soffeh, four-iwans, andChahartaq, and is observed in the buildings of the Qajar period as the basis of spatial arrangement.   Keyword:Architectural style, Traditional period, Geometry, Archetype, Formal pattern (form).     Introduction Contemporary Iranian architecture is influenced by the culture and lifestyle of European and Western countries, with a gradual change in the functionalism of interior spaces in the form of eliminating small spaces with different functions and reducing the size of the building. Therefore, examining architecture through historical studies of architectural periods of pre-Islamic and traditional buildings by selecting different examples and even paying attention to the analysis in the theories of Iranian architectural philosophers can help in providing a suitable explanation of the position of applied geometry and mathematics in the form of a formal pattern and achieving the goal of modular patterns resulting from the unity of elements under the influence of an effective unit in the design of functional and functional spaces. The stages of research in following the contemporaneity of architectural patterns of buildings from different historical periods and the interpretations of architectural theorists can be appropriate in achieving the goals. Art, architecture, and city design have long been intertwined with geometry in human culture. In Islamic culture, the expression of meanings and concepts in the form of simple and abstract shapes and motifs has always found a new expression. To the extent that the course of thought in the infinite world has led to the name of sacred geometry. On the other hand, the combination of some simple geometric shapes such as triangles, squares, and circles expresses broad symbolic concepts that are not limited to art and architecture. In particular, a wide range of shapes and meanings lies in the combination, integration, and division of these simple shapes (Tavasoli, 2004, p. 18).   Research Method Based on the research process in terms of how to examine the gradual changes in the architectural design of contemporary residential houses resulting from the ancient and traditional periods and the need to pay attention to the traditional architecture of the transitional period (Qajar) and the application of spatial organization characteristics and geometric order in different patterns in different regions of Iran and the superposition of Iranian and Islamic architectural values in providing a solution and achieving an optimal pattern, it is necessary to examine library studies and the research method in housing studies is interpretative-historical and descriptive-analytical in achieving the final model of Iranian housing. The method of collecting information is library (Table 1) and the research method is interpretative-historical and descriptive-analytical (Figure 1). The statistical population is historical monuments of the ancient and Qajar periods.   Chart (1). Research Method Chart   <ol> <li>A) Gradual developments in mathematics and geometry and their impact on architecture</li> </ol> From the review of historical studies in the pre- and post-Islamic periods in the theoretical foundations of research in the field of applied mathematics and geometry analysis and their impact on the architecture (industry) of buildings with residential use in different periods, the course of developments from the stages of the rational to the tangible and attention to numerical quantities and spatial qualities and the relationships between numbers and shapes in geometry, the results in Table (2) have been achieved.   Table (2). Characteristics of philosophers before and after Islam who had an impact on the sciences of mathematics and geometry   <table width="106%"> <tbody> <tr> <td width="6%"> Row. </td> <td width="12%"> application </td> <td width="20%"> Philosophy names </td> <td width="7%"> period </td> <td width="12%"> Books name </td> <td width="40%"> theory </td> </tr> <tr> <td width="6%"> 1 </td> <td rowspan="5" width="12%"> Geometry and theoretical mathematics </td> <td width="20%"> Thales </td> <td width="7%"> 527 B.C. </td> <td width="12%"> - </td> <td width="40%"> Mathematics, theorems (congruence of two triangles), equality of two angles in an isosceles triangle, height of triangular pyramids </td> </tr> <tr> <td width="6%"> 2 </td> <td width="20%"> Pythagoras </td> <td width="7%"> 600 B.C. </td> <td width="12%"> Philosophy </td> <td width="40%"> Geometry, numbers, shapes and music </td> </tr> <tr> <td width="6%"> 3 </td> <td width="20%"> Plato </td> <td width="7%"> 348 B.C. </td> <td width="12%"> The Epistle of Timaeus </td> <td width="40%"> Shapes and figurative numbers - pure and applied mathematics </td> </tr> <tr> <td width="6%"> 4 </td> <td width="20%"> Euclid </td> <td width="7%"> 300 B.C. </td> <td width="12%"> Plane geometry, principles </td> <td width="40%"> Algebra and number theory, linear proportions, phi number, golden ratio </td> </tr> <tr> <td width="6%"> 5 </td> <td width="20%"> Archimedes </td> <td width="7%"> 287 B.C. </td> <td width="12%"> - </td> <td width="40%"> Obtaining the number pi, statics, center of mass, Archimedes' solid (regular 13-sided) </td> </tr> <tr> <td width="6%"> 6 </td> <td rowspan="7" width="12%"> Geometry and practical mathematics </td> <td width="20%"> Al-Majusi-Khwarizmi(1) </td> <td width="7%"> 233 A.H. </td> <td width="12%"> Algebra and Counterfactual </td> <td width="40%"> Arithmetic and astronomy, distances between cities </td> </tr> <tr> <td width="6%"> 7 </td> <td width="20%"> Banu Musa (Muhammad, Ahmad and Hassan) </td> <td width="7%"> 300 B.C. </td> <td width="12%"> معرفه المساحت الاشکال البسطه و الکریه، الشکل المدور المستطیل </td> <td width="40%"> Angle trigonometry, calculating the volume and area of a circle (Pi), drawing an ellipse, the Wall of Dhul-Qarnayn in Gorgan, the Dar-al-Taj Observatory in Tigris, </td> </tr> <tr> <td width="6%"> 8 </td> <td width="20%"> Abū al-WafāBūzhjānī </td> <td width="7%"> 328 B.C. </td> <td width="12%"> هندسه ایرانی/ فی معرفه الابعاد بین المساکن/ فیما یحتاج الیه الصانع من الاعمال الهندسه </td> <td width="40%"> Regular polyhedron, Sinaat, Platonic shapes/Surface and distances of cities/Division of shapes/Drawing two-dimensional and three-dimensional shapes/Spherical geometry/Baghdad Observatory </td> </tr> <tr> <td width="6%"> 9 </td> <td width="20%"> Brethren of Purity </td> <td width="7%"> 400 B.C. </td> <td width="12%"> الرساله الجامعه </td> <td width="40%"> Numbers, Forms - The Sensible and Sensible World, Unity and Plurality, Sacred Number, Mysticism, Quality and Quantity/Morphology/Cosmology/The Pilgrim's Progress from This World/Wisdom and Craftsmanship </td> </tr> <tr> <td width="6%"> 10 </td> <td width="20%"> Naṣīr al-Dīn al-Ṭūsī </td> <td width="7%"> 597 B.C. </td> <td width="12%"> زیج ایلخانی، تذکره فی العلم الهیئه/ اشکال الکرویه/تجرید الهندسه/الشکل القطاع </td> <td width="40%"> Ethics, logic, mathematics, astronomy, philosophy, theology, the observatory and library of Maragheh </td> </tr> <tr> <td width="6%"> 11 </td> <td width="20%"> Ghiyāth al-DīnJamshīdMasʿūd al-Kāshī </td> <td width="7%"> 809 B.C. </td> <td width="12%"> رساله مفتاح الحساب/ رساله محیطیه/ رساله وتر و جیب </td> <td width="40%"> This school of astronomy,Samarkand/ Geometry and proportions </td> </tr> <tr> <td width="6%"> 12 </td> <td width="20%"> Baha al-Din Muhammad ibn Husayn al-Amili(1) </td> <td width="7%"> 953 B.C. </td> <td width="12%"> خلاصه الحساب (بحر الحساب) </td> <td width="40%"> Iranian geometry, Euclid's principles, proportion, equations, Naqsh-e Jahan Square, Isfahan </td> </tr> </tbody> </table>   <ol> <li>B) Study of examples of buildings from the ancient and traditional periods</li> </ol> Different buildings are listed in Table (3) according to the historical periods of the ancient and traditional periods, and from drawing the plan and examining the basic and archetypal patterns, the characteristics of the formal and functional patterns in each of the buildings are listed. The purpose of conducting studies in different buildings is to explain the course of historical developments in different periods and the gradual process of evolution of the four-faced and four-porch patterns until the end of the traditional period.     Table (3). The course of developments in the formal and functional patterns of spaces according to the use of archetypes in the ancient and traditional periods     Chart (3). The gradual trend of scientific developments in the application of geometry in buildings and urban planning     Conclusion - The manifestation of justice and fairness in the architecture of Iranian houses is sought in various geometric components, including harmony, balance, unity, proportions, limits and boundaries, symmetry, equilibrium, hierarchy, and static principles. Through the coordination of quantitative and qualitative aspects of geometry in architecture before and after Islam, the relationship between order and size with the justice of God and the unity of components is addressed. Excellence in Iranian architecture is provided by the adaptation of sensory and rational perceptions in explaining the defined factors of mathematics and geometry in the course of developments from theoretical application to practice and manifestation in the architectural industry. - The application of geometry in the architecture of buildings (temples) dates back to Egypt and Turkey (Assyrian civilization), respectively, which was in the eighth century BC, and studies have shown the transfer of techniques from Egypt to Iran and then Turkey, and following that, in the fifth century BC, the construction of the Parthenon Temple began, which was in line with the research of Thales, Pythagoras, and then Platonic volumes are investigated. - The study and research in the field of applied geometry in Iranian architecture, influenced by the experiences of the ancient period, reached its peak and flourishing by Iranian scientists and philosophers in the tenth century.   Footnote <ol> <li>1. In the 7th century AH, Khwaja Nasir al-Din Tus was one of the prominent figures. During the Mongol era, he established an observatory in Maragheh and engaged in research in natural sciences such as mathematics, astronomy, and geometry. It was in this observatory that the Zij al-Ilkhani was compiled, and under Tusi's supervision, almost all classical Greek mathematical works were translated into Arabic. Some of Khwaja Nasir's mathematical books include:</li> </ol> - The book Kashf al-Qana’ on the secrets of the shape of the sphere, this book was translated into French by Iskander Pasha Karateu Derry in 1891. - Al-Hisab Baltakht wa al-Tarab. This book was translated into Russian in 1963. - Al-Risalah al-Shafi’ah an al-Shak fi al-Khuti al-Mutawaziyyah. This book was translated into Russian by Rosenfeld in 1960. - The writing of Euclid’s Principles. - The writing of Archimedes’ Book of the Sphere and the Cylinder <ol start="2"> <li>Baha' al-Din Muhammad Ameli, known as Sheikh Baha'i, was a scholar during the reign of Shah Abbas Safavi. He was born in Baalbek in 953 AH. He immigrated to Iran with his father at the age of 13. He has written in Persian and Arabic, totaling 88 books and treatises. His works include Kashkul, Divan Ghazaliyat, Jame' al-Abbasi (in jurisprudence), Khalasat al-Hesab, Shashq al-Aflaq, and two famous Mathnavis, "Nan va Halwa" and "Shir va Shakar." He passed away in Isfahan in 1030 AH. His body was transferred to Mashhad and buried in the Goharshad Mosque.</li> </ol>   References Ardalan, N., & Bakhtiar, L. (2019) Sense of Unity (The Role of Tradition in Iranian Architecture). Tehran: New Thought Book. Akbari, F. (2016) Rethinking the Geometric Proportions of Creation in Works of Islamic Art and Architecture. Quarterly Journal of Urban Management Studies, 44, 107-124. Akbari, F., Pournamdarian, T., Shirazi, A., & Ayati, H. (2010) Spiritual Knowledge and Geometric Codes. Persian Language and Literature Research Journal, 1(13), 1-22. BalkhariGhahi, H. (2017) Geometry of Imagination and Beauty. Tehran: Matan Publications. Bahredar, A., Madani, R., & Afshari, M. (2014) Presenting the Physical Model of Today's Housing by Utilizing the Desirable Qualities of Historical Houses. Quarterly Journal of Sustainable Urban Development, 4(11), 33-50. Behzadpour, M. (1999) The Effect of the Central Courtyard on Culture and Family Solidarity. Interdisciplinary Studies in Management and Engineering (pp. 1-13). Tehran: University of Tehran. Pope, A. (1999) A Journey into Iranian Art. Tehran: Scientific and Cultural Publications. Pirnia, M. (1999) Research into the Past of Iranian Architecture. Tehran: Soroush Danesh. Tajvidi, A. (1966) The Contribution of Iranian Architecture to the Emergence of Islamic Architecture in the Early Hijri Centuries. Art and People, 4-5(47). Tavassoli, M. (1984) The Art of Geometry. Tehran: Payam Publications. Jazbeebi, S. (1989) The Application of Geometry in Practice. Tehran: Soroush Publications. JavadiNodeh, M., Shahcheraghi, A., & Andalib, A. (2022) A study of the golden proportions and geometric principles derived from nature in the physical components of historical houses. Bagh-e-Nazar, 35-48. Haeri Mazandarani, M. (2020) Titus Burckhardt's contribution to the understanding of Iranian architecture. Iranian Institute of Philosophy and Wisdom Research, 2-31. Hejazi, M. (2008) Sacred geometry in nature and Iranian architecture. History of Science (7), 17-44. Hosseinzadeh, L. (2022) A comparative study of the geometry of the central courtyard in the architecture of native houses of Shiraz. Interdisciplinary Studies of Iranian Architecture, 179-201. Hamzenejad, M. (2006) Man, Nature and Architecture. Tehran: University of Science and Technology. RezazadehArdebili, M., & Sabet Fard, M. (2013) Recognizing the application of geometric principles in traditional architecture. Fine Arts-Architecture and Urban Planning Journal, 29-44. Zarkesh, A. (2009) The role and influence of government factors in the architecture of private buildings in the first Pahlavi period. Book of the Month of Art, 14-25. Saeedi, P., & Salehi, A. (2001) Formalist references to the history of Iranian architecture in order to give identity to contemporary housing. Letter of Architecture and Urban Planning, 53-74. Shahriari, P. (2009) Biography and works of Abu Al-VafaBozjani. Islamic Research. Sheikhi, M., Momeni, K., &Wasigh, B. (2001) Geometric analysis and Iranian golden and golden proportions in the castle of Mir Gholam Hashemi of Ilam. Ilam Culture, 23(76-77), 24-38. Saremi, H., &Namnam, M. (2014) Decoding Geometry and Proportions in Iranian Architecture. National Conference on Architecture, Civil Engineering and Modern Urban Development. Saremi, A. (2010) Values of Iranian Architecture. Tehran: Cultural Heritage Publications. Tabatabaei, M. (2016) Designing Today's Houses in Continuation of Yesterday's Native House Patterns in the City of Zavareh. Isfahan: Faculty of Architecture and Urban Planning, Isfahan University of Art. Abbasi, N., GhasemiSichani, M., Vali Beig, N., &Saadoundi, M. (2019) Evaluation of the Opinions of Muslim Mathematicians (2nd to 11th Century AH) on the Nature of Geometry in Architecture. Architectural Thought, 3(5), 84-105. Gholamian, M., Agha Yazdanfar, S., & Norouzian Maleki, S. (2019) An approach to the common infrastructures underlying Iranian Islamic architecture. Scientific Hub of Islamic Architecture, 3-24. Karbasian, G., & Iran Talab, H. (2015) The combination of square and circular forms, the basic archetype in Iranian architecture. Modern research in civil engineering, architecture and urban planning. Tehran. Guthrie, D. (1996) History of Greek Philosophy (Pythagoras and Pythagoreans), translated by Mehdi Ghavam Safari. (M. Ghavam Safari, translator) Fekr Rooz Publications. Mohammadzadeh, N. (2016) Geometry and Proportions in Architecture. Mashhad: Aristotle Publications. Mardani, A., &Rusaei, A. (1997) The effect of the geometric pattern of the central courtyard on air flow in traditional houses of Shushtar. Islamic Iranian City, 71-102. Memarian, G. (1996) Introduction to Iranian Residential Architecture: Introverted Typology. Tehran: University of Science and Technology. Najafghalipour-Kalantari, N., Etesam, A., & Habib, F. (2017) A Study of Geometry and Golden Ratios in Iranian Architecture. Urban Management, 477-491. HashemiAzarvand, F. (2009) In Search of the Iranian House Pattern-Tehran City. Isfahan: Faculty of Architecture and Urban Planning, Isfahan University of Art. Danaeinia, A., Azad, M., &Khamehchian, A. (2019) The Role of Geometry of Yard in the Formation of the Historical Houses of Kashan. Mathematics Interdisciplinary Research, 21-35. F.Brock, J. (2004) Pyramids to Pythagoras: Surveying from Egypt to Greece (3000 B.C. to 100 A.D.). JARCE stands for Journal of the American Research Center in Egypt. Rapoport, A. (1972) Pour uneanthropologie de la maison. Paris: Beaudoux-Kovats Edith. Zolfagharzadeh, H., Jafariha, R., &Delzendeh, A. (2017) Different Ways of Organizing Space Based on the Architectural Models of Traditional Houses: A New Approach to Designing Modern Houses: (Case Study: Qazvin's Traditional Houses). Space Ontology International Journal, 17-31. https://www.ysma.gr/en/monuments/parthenon/ https://chinarmart.com/2022/03/12/the-digital-reconstruction-of-the-legendary-armenian-temple-of-haldi-in-musarir/ <a href="https://www.urartians.com.tr/alticerik/62/temples-and-religious-practices.html">https://www.urartians.com.tr/alticerik/62/temples-and-religious-practices.html</a>         <a href="#_ftnref1" name="_ftn1">*</a> Ph.D Student in Architecture, Tehran-West Branch, Islamic Azad University, Tehran, Iran. projecthatami2020@gmail.com <a href="#_ftnref2" name="_ftn2">**</a> Corresponding Author: Professor of Architecture Department, Tehran-Central Branch, Islamic Azad University, Tehran, Iran. emarate_khorshid@yahoo.com <a href="#_ftnref3" name="_ftn3">***</a> Professor of Art and Theater Department, Tarbiat Modares University, Tehran, Iran. mokhtabm@modares.ac.ir <a href="#_ftnref4" name="_ftn4">****</a> Assistant Professor of Architecture Department, Tehran-West Branch, Islamic Azad University, Tehran, Iran. zare.leila@gmail.com    نقش و اهمیت تأثیر هندسه و ریاضیات در معماری ایران از دوران پیش از اسلام در قالب معماری تکنیک (تجربی) و الگو (مَندَل) به&zwnj;صورت کاربرد عملی در انتظام هندسی بناها به&zwnj;کار رفته است. در بسیاری از بناها با کاربری حاکمیت، تشریفاتی- سکونتی، مسکونی به&zwnj;ترتیب از طبقات اجتماعی خواص و عوام در دوران باستان و  بعد از اسلام؛ قرن چهارم تا دهم ه.ق مشاهده شده است و رویکرد تأثیرات در فضاهای عملکردی و پیروی از الگوهای اولیه در سبک معماری ایرانی به&zwnj;عنوان کارکردهای فضایی اندرونی و بیرونی بیان می&zwnj;شود. مطالعات سیر تحولات تاریخی نشان می&zwnj;دهد که معماری مسکونی در ایران از  به&zwnj;کارگیری الگوی شکلی به&zwnj;عنوان چیدمان فضایی در نمونه بناهایی از سه دوره تاریخی از دوره باستان، سنت و مدرن حاصل شده است. در این پژوهش جمع&zwnj;آوری داده&zwnj;ها به&zwnj;صورت کتابخانه&zwnj;ای و روش تحقیق از نوع تفسیری-تاریخی، توصیفی-تحلیلی است. هدف پژوهش تبیین تأثیر تحولات الگوهای شکلی در قالب صناعات معماری است که تحت&zwnj;تأثیر هندسه کاربردی و ریاضیات است که مطالعات فلاسفه ایرانی از جمله خوارزمی، بنوموسی، ابوالوفا بوزجانی، اخوان الصفا، خواجه نصیرالدین طوسی و شیخ بهائی آن را تقویت می&zwnj;نماید. همچنین از شروع قرن سوم هجری قمری تحت&zwnj;تأثیر مباحث ریاضیات و هندسه با پیروی از اعداد و تخمین مسافت، هندسه در قالب بعد دوم، بعد سوم و در نهایت صناعت معماری و معانی عرفانی و سیر و سلوک و تعالی (معقولات-محسوسات) در ترکیب انتظام اشکال و احجام افلاطونی در اماکن مذهبی نمود می&zwnj;یابد. نتایج پژوهش نشان می&zwnj;دهد که کاربرد الگوی مبنا در بناهای مسکونی با تأثیر از کاربرد ریاضیات و هندسه در معانی شکلی و مدولار ایرانی است که منشا اولیه از چهار صُفه و چهار ایوانی و چهار طاقی داشته است و در بناهای دوره قاجار به&zwnj;عنوان مبنای چیدمان فضایی مشاهده می&zwnj;شود.

http://iic.ihss.ac.ir/ar/Article/Download/48608