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Mathematical Treasures of Japan in the Edo Period

Frank J. Swetz (Pennsylvania State University)


This article was inspired by the 2011 exhibit and website Japanese Mathematics in the Edo Period, produced by the National Diet Library of Japan. The Edo Period of Japanese history is generally considered to span the years 1603-1867 CE. The National Diet Library exhibit focused on Wasan, which Sato Ken'ichi and Orita Hiroharu, in their Introduction to the online version of the exhibit, defined as "the indigenous mathematics of Japan" and as "the mathematics that developed in Japan before the Edo period, independently from Western mathematics." This is not to say that indigenous mathematical development ceased during the Edo period; in fact, "Wasan was at its peak" during this period, with many scholars making great progress and many books produced. Nor does the exhibit ignore the influence of Western scholarship during the period: in Chapter 1. Early Edo Period, the exhibit authors wrote that the gradual incursion of Western mathematics resulted in Wasan being "replaced by its Western counterpart immediately after the start of the Meiji era" (1868-1912).

We begin with sangi, or counting, rods first used in China and, subsequently, in Korea and Japan.

Sangi Rods and Computing Surface

Sangi rods and a computing surface, like those shown below, were used for calculations in Edo Period Japan.

The Japanese system of computing using sangi rods was adopted from the Chinese. The Chinese rods were called saunzi. The characters across the top row of the inscription designate number groupings. For the rod configuration shown, the row entries reading right to left designate units, tens, and hundreds. Thus, the rod configurations appear to be addends for a sum. Reading down the columns: “23 + 144 + 48 + 1.”

To view a set of counting rods from Korea, see Mathematical Treasures – Korean sangi rods, here in Convergence

The image above is presented through the kind cooperation of the National Diet Library, Japan, and is used with permission. It was obtained from the library’s digital gallery exhibit, Japanese Mathematics in the Edo Period.

See the list below for additional information about and images of mathematical texts and tools from the Japanese Edo Period, presented as "pages" in this Convergence digital "book." For texts from other institutions and cultures, see our Index of Mathematical Treasures; to find other tools and instruments, check our Index of Mathematical Objects.

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasures of Japan in the Edo Period," Convergence (July 2018), DOI:10.4149/Convergence20180721