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Investigating the mathematical and geometric principles embedded in ancient classic architecture is a significant tradition in the history of architectural development. Drawing inspiration from the modular design and creative ideology based on the geometric proportions of squareness and roundness in ancient Chinese architecture, we propose a new mode of squareness and roundness composition based on scale proportion specifically for the design of multi-story buildings. Taking Yingxian Wooden Pagoda as the case study, we not only re-evaluate the modular system and proportional rules followed in the design of the entire pagoda, but also reveal the technical approaches and geometric rules for effectively controlling the form of multi-story buildings. In particular, the mode of squareness and roundness composition based on scale proportion, utilizing a modular grid combined with squareness and roundness drawings as decision-making tools, can control the scale and proportion of buildings across different design dimensions and organically coordinate the design of multi-story buildings’ plans and elevations. Thus, it can achieve an effective balance of multi-story architectural forms. This study has potential applications in the creation of traditional multi-story buildings and heritage restoration projects, and offers valuable insights for future research on ancient multi-story buildings. Full article

Pagodas and pavilions (ge 閣) are the most popular and representative multi-story buildings since Buddhism was introduced to China. While providing visitors with a new visual experience, they have also largely reshaped the urban space and skyline in medieval China. The former originated from India and Central Asia and was transformed in China, developing a unique style; The latter originated more from the creation of Chinese architects and became a model of typical Chinese-style Buddhist architecture. Briefly, the pagoda matured earlier than the pavilion, and continuously developed while maintaining its basic style; the pavilion-style Buddhist architecture gradually developed later and finally matured after the Tang and Song dynasties (618–1276), partially presenting a different spatial logic from the pagoda, and bringing a new visual experience. In my opinion, although the pavilion may not necessarily be as large as the pagoda in terms of volume and absolute height, it can provide believers with greater visual impact in the internal space for worship, due to the cross-story giant Buddhist statues; the closer integration of Buddha statues and architecture makes it replace or share the core position of the pagoda in some monasteries and even become the visual center of the entire religious space. Due to the existence of the pavilion, viewers can not only worship the Buddhist statues on a two-dimensional plane or by looking up at the statues from the bottom, but have also gained a three-dimensional perspective, to worship directly at the Buddha’s shoulders, neck, and head. In the Buddhist grottoes, the layout of the early single-layer or multi-layer horizontally distribution of caves on cliff was also changed due to the excavation of the cross-layer giant statue grottoes, covered by multi-story pavilion-style buildings, providing viewers with a visual experience similar to that of the pavilions of great statues. Additionally, there is a new visual experience of worshiping the Buddha in a vertical circle, in cases such as Bamiyan and the Leshan Giant Buddha. Full article

In this study stone pagodas from ancient Japan (7th to 9th centuries) were analyzed. The findings show that there are some apparently influenced by the Korean Peninsula and two other types. While there are examples of the former type that are large and serve as temple buildings, the latter are located in mountain forest temples. I am of the opinion that stone pagodas were important mechanisms that made possible the existence of mountain forest temples as Mahayana precepts-based transgression repentance (keka 悔過) training sites that complemented flatland temples. This use of stone pagodas is different than China and Korea, which treated both wooden and stone pagodas in the same way. Moreover, ideas regarding Mahayana precepts-based transgression repentance were introduced from China, and I hold that the increase in stone pagodas at mountain forest temples corresponds to the Sinicization of Japanese Buddhism. Full article