Mathematics of Carpentry in Historic Japanese Architecture

Abstract

In traditional Japanese buildings, carpenters retained traditional ways of construction; once clients and a master carpenter decided the size and Kiwari of the project, almost all other design and structural systems were automatically fixed. At the beginning of the nineteenth century, master carpenter and mathematician Heinouchi Masaomi wrote theories of Kikujutu (Architectural Stereotomy), and used his knowledge of Japanese historical mathematics, Wasan, as well as Western mathematics to analyze the technology of carpentry. However, as the nature of Wasan is very different from Western mathematics, the role of geometry and algebra in the carpenters’ knowledge to create Japanese historical architecture was reinterpreted in Heinouchi’s text. This study explains the varieties and subtleties in the creation of architectural forms with Wasan before Heinouchi, and how and why they were transformed by him.