Reconsidering a proportional system of timber-frame structures through ancient mathematics books: a case study on the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery

Abstract

ABSTRACTThe mathematics references in ancient China, the Zhoubi Suanjing and the Jiuzhang Suanshu, present information on formative ideas of ancient people and their perception of objects. The introduction to the Yingzao Fashi mentions mathematical sources, including the Zhoubi Suanjing. Both of these books focus on the philosophical concept of Tianyuan difang (Heaven is round and Earth is square), as well as inscribed and circumscribed circles. The square root of 2(√2), which can be derived from this part, proves to be an essential criterion for building, seen in Korea, China, and Japan. Using the exemplary Koryŏ building, the Muryangsujŏn Hall at Pusŏksa Buddhist Monastery, this thesis shows that the standard ground plan width of the outermost bay has a √2 ratio to the central bay width. Its cross-section, likewise, proves that √2 times or twice the distance or height (relying on the height of the eave columns) are applied to the distance or height between each column and purlin in the application of arithmetic and geometric concepts. In the future, this work will be a reference for the reconstruction design of ancient buildings prior to the Koryŏ period, analogous to the Muryangsujŏn Hall.