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Mathematical Treasures of Japan in the Edo Period: Geometry

Frank J. Swetz (Pennsylvania State University)

Shoho kongen is a geometry text focusing on obtaining the volumes of various polyhedra. It is assumed to have been compiled by the mathematician Matsunaga Yoshisuke (1692-1774) and employs dissection techniques to derive formulae for volumes. Instruction begins on the title page.

A convex polyhedron is subjected to several dissections.

The tetrahedron is examined in detail.

The frustum of a square pyramid is subjecting to “cutting”. The ancient Egyptians used similar methods in studying the properties of pyramids.

An example of “cutting corners”:

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: Geometry," Convergence (July 2018)