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Mathematical Treasures of Japan in the Edo Period: Arithmetic and Algebra

Frank J. Swetz (Pennsylvania State University)

Shinpen sangaku keimo (1690) is a reprinting of the Chinese work, Suanxue qimeng (1299), by Zhu Shijie (c.1260-1320). The Japanese mathematician Takebe Katahiro (1664-1739) added a commentary. The work teaches basic arithmetic operations and Chinese algebraic solution methods, or tian yuan shu, for solving polynomial equations of higher degree. The title page is shown below.

Problem calculations and explanations are carried out using rod numerals:

These images are presented through the kind cooperation of the National Diet Library, Japan, and are used with permission. They were obtained from the library’s digital gallery exhibit, Japanese Mathematics in the Edo Period, where a complete examination and viewing of the item presented above can be found.

Index to Mathematical Treasures

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasures of Japan in the Edo Period: Arithmetic and Algebra," Convergence (July 2018)