Japanese mathematics

Wasan (Japanese和 算, dt as: " Japanese Mathematics" ) is the Japanese term for those in Japan during the Edo period (1603-1867 ) operated traditional form of mathematics. The western form of mathematics is in contrast to this, called Yosan (洋 算, "Western mathematics ").

History and content

Wasan was under the influence of Chinese mathematics books, which came towards the end of the 16th century through Korea to Japan, especially Suanxue Qimeng (Chinese算 学 启蒙, Introduction to mathematical studies ') of Zhu Shijie and Suanfa (Chinese算法, methods of mathematics ') of Yang Hui, as well as to the Han - time reaching back Jiuzhang SuanShu (Chinese九章 算术, the nine chapters of mathematical art '). These were commented first, but subsequently supplemented or replaced by independent developments of the Japanese mathematician.

Contents of Wasan were questions that you the areas Analysis, algebra, combinatorics, number theory or geometry assigns from today's perspective. The independent contributions of Wasan (but not in its full generality ) include the development of different, by the Chinese acquired algebraic and numerical techniques (eg, Horner's scheme), the introduction of determinants and the Enri (円 理, dt "circle principle "), which partly represents an analogue of the Western calculus. Using these findings, it initially succeeded Japanese mathematicians in 1700, the number to 10 digits to accurately determine ( Seki Takakazu ), during the 18th century, even at 50 points ( 25 points Kamata (1730? ), 41 points Takebe Katahiro (1723 ), 50 points Ryōhitsu Matsunaga ( 1739 ) ).

Wasan books to Chinese tradition differ significantly in structure and following the style of contemporary Western mathematics books; they are broken down by specific problems, which are discussed separately. They are not structured according to a theoretical superstructure and do not have oriented on Euclid, built on axioms definition - theorem-proof scheme. Another typical peculiarity of Wasan books is the Idai. Here unsolved problems are formulated at the end of the book, which can be taken up and processed by other mathematicians.

Another aspect of Wasan time was the Sangaku (Japanese算 额, literally meaning " mathematical panel / tablet "). This was at wooden panels on which geometric puzzles have been described. These were hung in temples as an offering or to the intellectual challenge of the pilgrims. Sangaku was practiced not only by scholars, but by all social classes.

From 1868 Wasan as part of the reforms of the Meiji government by Western mathematics ( Yosan ) was replaced.

Significant representatives

• Mōri Shigeyoshi (also called Mōri Kambei ): Developed the arithmetic methods for the Soroban (Japanese abacus ).
• Yoshida Mitsuyoshi (1598-1672)
• Seki Takakazu (1642-1708)
• Takebe Katahiro (1664-1739)
• Matsunaga Ryōhitsu (fl. 1718-1749 )
• Kurushima Yoshita (d. 1757)
• Arima Raido (1714-1783)
• Ajima Naonobu (1739-1783)
• Aida Yasuaki (1747-1817)
• Sakabe Kohan (1759-1824)
• Hiroshi Hasegawa ( 1782/83-1838 )
• Wada Yasushi (1787-1840)
• Shiraishi Nagatada (1796-1862)
• Koide Shuki (1797-1865)
• Omura Isshu (1824-1871)
• Satō Seiko