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The Sakyamuni Pagoda of Fogong Temple, also known as the Yingxian Wooden Pagoda or the Wooden Pagoda of Ying County, is China’s oldest and tallest wooden pagoda. This pagoda was constructed in 1056 and has faced many challenges, including earthquakes, wars, and mistreatment. However, it is currently in danger of potential collapse due to severe structural challenges. Preserving this historic monument requires interdisciplinary collaboration across architectural history, materials science, and engineering. This paper proposes the development of a parametric model to build the pagoda that can be used for future preservation efforts. While not precisely reflecting the pagoda’s current condition, with the changes in inputs, the geometries of the structural members can be updated in real time, which offers adaptability crucial for preservation efforts. With the understanding of the original construction techniques, including its leaning column systems, the model not only helps preservation but also reveals the creativity of the architects or the craftsmen at the time. The 3D model, which includes more than 32,000 pieces along with the parametric files that can generate the column grid and dougongs, has been published along with this paper, and those files are available in the Data Availability Statement. In summary, the full digital model presented alongside this paper, unavailable elsewhere to the general public, serves as a practical preservation tool that can also be used for raising awareness for this cultural heritage site. Full article

In Ying Xian Fogong Si Shijia Ta 應縣佛宮寺釋迦塔 (Sakyamuni Pagoda of Fogong Temple in Ying County), Shanxi, there are statues set on each floor, and 26 exist in total, with six murals painted on the first floor. The pagoda was designed as a vertically rising Buddhist temple, and the interior space of each floor was customized for the statues. Based on previous research and through surveying and mapping of the architecture and statuary (including the murals on the first floor) combined with geometric design analysis, this paper proposes the following: First, there exists a clear geometric proportion among the interior space and statues on each floor of the pagoda. Second, clear proportional relationships also exist among the statues on each floor, and each of the 26 statues has ‘classical’ proportion rules. Third, the height of the giant Buddha statue on the first floor is the module for not only the height of the statues on each floor but also the construction of the whole pagoda such that the height of the statue on the first floor is 1/6 of the total height of the pagoda (excluding the base). And the ratio of the pagoda’s total height to the first floor’s diameter, the ratio of the total height to the top-story height under the column capital, and all the other geometric proportions are closely related to the architectural modeling. And finally, in the construction of the pagoda, statues, and murals, the scale is deduced to be 1 chi 尺 (Chinese foot) = 29.5 cm. These values give clear scale logics not only to the construction but also to the details of the statues. Accordingly, the most frequently used proportions in the architectural space, statues, and murals of the Pagoda of Fogong Temple are $\sqrt{2}$, 3:2, 5:3 (or 8:5), and 9:5, which are imbued with cultural messages, like Zhou Bi Suan Jing 周髀算經 (The Mathematical classic of the Zhou shadow-gauging instrument), Ying Zao Fa Shi 營造法式 (Treatise on Architectural Methods or State Building Standards), the ancient Chinese world view—tian yuan di fang 天圜地方 (the dome-shaped heaven and the flat, square earth) reflected from “ yuan fang tu 圓方圖 (rounded-square map)” and “fang yuan tu 方圓圖 (squared-circle map)”, ancient Chinese ideas that ”san tian liang di er yi shu 參天兩地而倚數 (‘three’ is the number of the heaven and ‘two’ is the number of the earth, and all numbers are based on them)” and “jiu wu zhi zun 九五之尊 (nine and five are the numbers of the honorable central position)”, and most probably related to the “mandala” of Esoteric Buddhism and to the Western “Golden Ratio”, which all need further research in depth. Full article