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Sangaku Proofs: A Japanese Mathematician at Work

CEAS 175 Sangaku Proofs cover
J. Marshall UNGER
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During many decades of national isolation, a mathematical tradition called wasan flourished in Japan independently of the advances of Enlightenment mathematics and virtually unknown to Europeans before the Meiji Restoration. Yet the brilliance of its practitioners, the wasanka, would surely have been admired by Leibniz or Euler had they been able to read their solutions to often difficult geometry problems. This interpretive translation of a suite of twenty-six related problems analyzed by Aida Yasuaki (1747–1817) gives readers unfamiliar with the premodern Japanese language access to a real wasan text. Instead of presenting and solving problems using modern techniques, Unger presents Aida’s own solutions, transcribing his calculations into familiar mathematical notation, highlighting connections between Aida’s work and both the mathematics of today and aspects of Japanese cultural history. A specialist in the history of the Japanese language, he aims to bring fellow amateur mathematicians and interested professionals into contact with actual wasan methods, and to initiate a discussion of how wasan fits into the larger picture of premodern Japanese history.

Press Note: Since printing we discovered two errors that went uncorrected on pages 2 and 48. Please download the two affected pages to replace those in your book. On page 2, 16A should be 16A2; on page 48, the alpha symbol should be l02. We regret the inconvenience. The volume has been reprinted with corrected pages as of July 2015.


  • J. Marshall UNGER is professor of Japanese at Ohio State University. His research has focused on the history of Japanese, teaching Japanese as a second language, and writing systems of East Asia. Two of his books, The Fifth Generation Fallacy and Literacy and Script Reform in Occupation Japan, are available in Japanese.

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