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Paper short abstract

Sangaku, votive tablets with mathematical problems, became popular during Japan's national seclusion; many problems were also reproduced in printed collections. The talk will discuss the dynamics caused by this twofold existence of sangaku problems within Edo Japan's mathematical community.

Paper long abstract

During the Edo period's national seclusion, Japan developed its own form of mathematics, retroactively dubbed wasan, complete with its bespoke social medium: sangaku, votive tablets featuring mathematical problems in word and image, dedicated in temples and shrines across the country. Today, over 900 sangaku are still recorded as extant; approximately 1500 problems from lost sangaku have been documented in manuscripts and printed books – the majority of which date back to the late 18th and early 19th century.

Sangaku were not the only ema recorded in scriptural sources. But whilst books like the Miyako ema kagami (1819) or the Itukushima ema kagami (1830) try to render the original object as accurately as possible, including the frame and a vernacular description, sangaku were rarely reproduced as complete objects. Rather, printed collections of select sangaku problems, most prominently Fujita Kagen's Shinpeki sanpō (1789) and Zoku shinpeki sanpō (1807), were used to propagate problems of interest beyond the local confines of the actual tablet. Whilst the original sangaku often boast artistic elements or colourful diagrams, the printed versions simply reproduce the geometric shapes that make up the problem in black and white, complete with the original problem statement in Kanbun. As that, select components of a sangaku could develop their own dynamic and reach far-flung mathematical communities, without their members ever having to set a foot in the actual place of dedication.

Proposed contribution will discuss the ramifications of this two-fold existence of sangaku as a medium of communication – and how the physical object's enhanced reach could promote response, emulation and reciprocation in the expert community.