ARCHITECTURAL DESIGNS INSPIRED BY NATURE AND MATHEMATICAL MODELS

Aslı Taş, Güneş Mutlu Avinç

Abstract


Introduction: This paper explores how nature-inspired mathematical models and principles are applied in architectural design and how these approaches contribute to innovative and sustainable solutions. Architectural structures incorporating nature-inspired and mathematical models have been widely studied in the literature. However, research examining the relationship between nature and mathematics specifically within the field of architecture remains limited. Addressing this gap, the study investigates the interplay between mathematics and nature in architectural design. Its contribution lies in providing a holistic examination of mathematical models in architecture. Within the scope of the study, five examples demonstrating different mathematical theorems were analyzed. Methods: The structures were evaluated using qualitative content analysis, while the mathematical models were identified through visual content analysis. The findings are summarized in a table. Conclusion: Architecture is profoundly shaped by the relationship between nature and mathematics. Analyzing the mathematics inherent in nature and applying these principles in design serves as a guide for creating aesthetically pleasing, sustainable, and innovative buildings.

Keywords


mathematical model, nature-inspired architecture, golden ratio, fractal geometry, mathematics in architecture

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References


Aejaz, S. and Yasmeen, A. (2023). The importance and applications of mathematics in architecture. International Journal of Current Science (IJCSPUB), Vol. 13, Issue 1, pp. 848–887. DOI: 10.13140/RG.2.2.19605.29923.

Akhtaruzzaman, M. and Shafie, A. A. (2011). Geometrical substantiation of Phi, the golden ratio and the baroque of nature, architecture, design and engineering. International Journal of Arts, Vol. 1, No. 1, pp. 1–22. DOI: 10.5923/j.arts.20110101.01.

APA Facade Systems (2015). The Bergeron Centre for Engineering Excellence, York University, Canada. [online] Available at: https://www.apafacadesystems.com/wp-content/uploads/2017/09/York-University-Lassonde-School-of-Engineering-19_Easy-Resize.com_.jpg [Date accessed 12.08.2025].

Architecturestudio (2021). Institut du Monde Arabe. [online] Available at: https://architecturestudio.fr/wp-content/uploads/2021/07/architecturestudio_pastb1_4-2200x1483.jpeg [Date accessed 12.08.2025].

Attia, A. S., Hussein, M. T., and El Shaer, N. S. E. D. (2021). The Grand Egyptian Museum: implications for sustainability. The International Journal of Tourism and Hospitality Studies, Vol. 1, Issue 2, pp. 13–24. DOI: 10.21608/ijthsx.2021.82482.1009.

Bergil, M. S. (1993). Doğada Bilimde Sanatta Altın Oran. İstanbul: Arkeoloji ve Sanat Yayınları, 192 p.

Besix.com (2022). [online] Available at: https://www.besix.com/en/projects/grand-egyptian-museum [Date accessed 12.08.2025].

Bovill, C. (1996). Fractal geometry in architecture and design. Boston: Birkhauser Verlag, 195 p.

cdn.sortiraparis.com (2021). Institut du Monde Arabe. [online] Available at: https://cdn.sortiraparis.com/images/80/47294/197171-jardin-d-orient-a-l-institut-du-monde-arabe.jpg [Date accessed 11.08.2025].

Chandra, S., Körner, A., Koronaki, A., Spiteri, R., Amin, R., Kowli, S. and Weinstock, M. (2015). Computing curved-folded tessellations through straight-folding approximation. In: Samuelson, H., Bhooshan, S., Goldstein, R. (eds.). SimAUD ‚15: Proceedings of the Symposium on Simulation for Architecture & Urban Design. San Diego: Society for Computer Simulation International, pp. 152–159.

Cheng, F., Wu, X.-J., Hu, Z., Lu, X., Ding, Z., Shao, Y., Xu, H., Ji, W., Wu, J., and Loh, K. P. (2018). Two-dimensional tessellation by molecular tiles constructed from halogen–halogen and halogen–metal networks. Nature Communications, Vol. 9, 4871. DOI: 10.1038/s41467-018-07323-6.

Cooper, J. M. (ed.) (1997). Plato. Complete works. Indianapolis, Cambridge: Hackett Publishing Company, 1808 p.

Egypt Forward (2023). Grand Egyptian Museum. [online] Available at: https://egyptfwd.org/Article/6/5718/The-completion-ofplacing-more-than-50-of-the-heavy [Date accessed 11.08.2025].

en.wikiarquitectura.com (2017). Villa Cook. [online] Available at: https://en.wikiarquitectura.com/villa_cook_3-2/ [Date accessed 11.08.2025].

Front Desk (2014). Le Corbusier - Villa Stein, Garches. [online] Available at: https://frontdesk.co.in/forum/Thread-Le-Corbusier-Villa-Stein-Garches?pid=1177 [Date accessed 12.08.2025].

Gazi, A. and Korkmaz, K. (2015). Tesselasyon kullanarak genişleyebilen strüktür tasarımı. In: Uluslararası Katılımlı 17. Makina Teorisi Sempozyumu, İzmir, Turkey, June 14–17, 2015.

Grünbaum, B. and Shephard, G. C. (1987). Tilings and patterns. New York: W. H. Freeman and Company, 700 p.

Hacısalihoğlu, H. H. (2015). Fraktal geometri. Ankara: Seçkin Yayıncılık, 160 p.

Hagerhall, C. M., Purcell, T., and Taylor, R. (2004). Fractal dimension of landscape silhouette outlines as a predictor of landscape preference. Journal of Environmental Psychology, Vol. 24, Issue 2, pp. 247–255. DOI: 10.1016/j.jenvp.2003.12.004.

Herz-Fischler, R. (1984). Le Corbusier’s “regulating lines” for the Villa at Garches (1927) and other early works. Journal of the Society of Architectural Historians, Vol. 43, Issue 1, pp. 53–59. DOI: 10.2307/989975.

images.adsttc.com (2018). Toronto Engineering School. [online] Available at: https://images.adsttc.com/media/images/5670/ca23/e58e/ce8c/5500/02b7/slideshow/ZAS_bergeron-055-Pano-Edit.jpg?1450232335 [Date accessed 11.08.2025].

Kavurmacıoğlu, Ö. and Arıdağ, L. (2013). Strüktür tasarımında geometri ve matematiksel model ilişkisi. Beykent University Journal of Science and Engineering, Vol. 6, Issue 2, pp. 59–76.

Kolarevic, B. (2003). Architecture in the digital age: design and manufacturing. New York, London: Taylor & Francis, 320 p.

Kornev, A. P. (2018). Self-organization, entropy and allostery. Biochemical Society Transactions, Vol. 46, Issue 3, pp. 587–597. DOI: 10.1042/BST20160144.

lookphotos (2008). France, Paris, Institut du Monde Arabe (Arab World Institute) by architect Jean Nouvel and Architecture studio. [online] Available at: https://www.lookphotos.com/en/images/71117694-France-Paris-Institut-du-Monde-Arabe-Arab-World-Institute-by-architect-Jean-Nouvel-and-Architecture-studio [Date accessed 10.08.2025].

Mandelbrot, B. (1982). The fractal geometry of nature. San Francisco: W. H. Freeman and Company, 460 p.

Marples, C. R. and Williams, P. M. (2022). The golden ratio in nature: a tour across length scales. Symmetry, Vol. 14, Issue 10, 2059. DOI: 10.3390/sym14102059.

McKiernan, M. (2013). Jean Nouvel, Arab World Institute, 1987. Occupational Medicine, Vol. 63, Issue 8, pp. 524–525. DOI: 10.1093/occmed/kqt123.

Nowak, A. (2015). Application of Voronoi diagrams in contemporary architecture and town planning. Challenges of Modern Technology, Vol. 6, No. 2, pp. 30–34.

Nowak, A. and Rokicki, W. (2016). On surface geometry inspired by natural systems in current architecture. Journal Biuletyn of Polish Society for Geometry and Engineering Graphics, Vol. 29, pp. 41–51.

orascom.com (2023). Grand Egyptian Museum. [online] Available at: https://orascom.com/wp-content/uploads/1202-1366x768.jpg [Date accessed 10.08.2025].

Ostwald, M. J. and Williams, K. (2015). Relationships between architecture and mathematics. Architecture and Mathematics from Antiquity to the Future. Volume 1: Antiquity to the 1500s, pp. 1–21. DOI: 10.1007/978-3-319-00137-1_1.

Peker, A. U. (2017). Altın oran ve mimarlık: efsane ve gerçekler. BÜMED, No. 231, pp. 46–47.

Rian, I. M., Park, J.-H., Ahn, H. U., and Chang, D. (2007). Fractal geometry as the synthesis of Hindu cosmology in Kandariya Mahadev temple, Khajuraho. Building and Environment, Vol. 42, Issue 12, pp. 4093–4107. DOI: 10.1016/j.buildenv.2007.01.028.

Sack, J. R. and Urrutia, J. (eds.) (1999). Handbook of computational geometry. Amsterdam: Elsevier Science B. V., 1075 p.

Salvadori, M. G. (1968). Mathematics in architecture. Englewood Cliffs: Prentice Hall, 173 p.

Trubiano, F. (2013). Performance based envelopes: a theory of spatialized skins and the emergence of the integrated design professional. [online] Available at: https://www.researchgate.net/publication/307671319/figure/fig2/AS:406346466906113@1473891955371/Water-Cube-Project-in-Beijing-China-ARUP-Associates-Courtesy-Terri-Boake-University.png [Date accessed 11.08.2025].

URL-1: https://www.zasa.com/york-engineering-2 [Date accessed 11.08.2025].

Vassilev, T. S. and Eades, B. (2013). Generalizations of the Voronoi Diagram. American Journal of Computational and Applied Mathematics, Vol. 3, No. 2, pp. 91–96. DOI: 10.5923/j.ajcam.20130302.06.

w.litour.cn (2018). Water Cube, Beijing. [online] Available at: https://w.litour.cn/img/beijing/water-cube/water-cube-1.jpg [Date accessed 11.08.2025].

Wood, B. (2020). An apartment in Le Corbusier’s iconic Villa Stein is for sale. [online] Available at: https://thespaces.com/anapartment-in-le-corbusiers-iconic-villa-stein-is-for-sale/ [Date accessed 12.08.2024]. Wordpress (2013). Water Cube. [online] Available at: https://wanba001.wordpress.com/wp-content/uploads/2013/11/e68d95e88eb7.jpg [Date accessed 10.08.2025].

Zhao, G., Denisova, K., Sehatpour, P., Long, J., Gui, W., Qiao, J., Javitt, D. C., and Wang, Z. (2016). Fractal dimension analysis of subcortical gray matter structures in schizophrenia. PloS One, Vol. 11, No. 5, e0155415. DOI: 10.1371/journal.pone.0155415.

Zou, P. X. W. and Leslie-Carter, R. (2010). Lessons learned from managing the design of the ‘Water Cube’ National Swimming Centre for the Beijing 2008 Olympic Games. Architectural Engineering and Design Management, Vol. 6, Issue 3, pp. 175–188. DOI: 10.3763/aedm.2010.0114.


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