Morphological Study on Multi-storied Brick Pagodas of the Tang Dynasty: An Analysis Method Based on Historical Patterns and Mathematical Models

This morphological study of multi-storied brick pagodas of the Tang Dynasty expands studies of the design theories of traditional masonry towers. Through a comprehensive examination of the formal beauty and design principles of ancient Chinese architecture, we identified and verified square-circle patterns (special intersectional relationships between squares and circles in geometry) and the dimensional modulus used in the morphological design of multi-storied brick pagodas of the Tang Dynasty. According to the linear variation characteristics of the geometric shapes of the brick pagodas, a linear regression analysis was conducted to identify the relationships among the dimensions of the most typical Tang multi-storied brick pagoda, the Xuanzang Pagoda in Xi’an. A set of mathematical models was then formulated through parametric abstraction to describe these relationships. These models were confirmed plausible for describing other Tang multi-storied brick pagodas involved in the study. In addition, the use of proportion and modules implies that there is the possibility that the design of multi-storied brick pagodas in the Tang dynasty took other wooden structures as a reference. Our study provides a new scientific research method for the design and protection of pagodas, and is useful for future studies of ancient Chinese multi-storied buildings.