Wasan
Wasan ( Japanese. 和 算 , English: "Japanese mathematics") is the Japanese name for the traditional form of mathematics practiced in Japan during the Edo period (1603–1867) . The western form of mathematics is called Yōsan ( 洋 算 , "western mathematics") to differentiate it .
History and content
Wasan created under the influence of Chinese mathematics books in the late 16th century over Korea to Japan reached, especially Suanxue Qimeng ( Chinese 算學啟蒙 - "Introduction to Mathematical Studies") by Zhu Shijie and suanfa ( Chinese 算法 - "Methods of Mathematics" ) by Yang Hui as well as Jiuzhang Suanshu ( Chinese 九章 算術 - “The 9 chapters of the mathematical art”), which goes back to the Han period . These were initially commented on, but subsequently supplemented or replaced by independent further developments by Japanese mathematicians.
The contents of the Wasan were questions that from today's perspective can be assigned to the areas of analysis , algebra , combinatorics , number theory or geometry . The independent contributions of Wasan include the further development of various algebraic and numerical techniques adopted by the Chinese (e.g. the Horner scheme ), the introduction of determinants (but not in their full generality) and the Enri ( 理 理 , Eng. "circle principle"), which is partly an analogue to the western calculus . With the help of this knowledge, Japanese mathematicians were able to determine the number to 10 digits ( Seki Takakazu ) first around the year 1700, and in the course of the 18th century even to 50 digits (25 Kamata (1730?), 41 Takebe Katahiro) (1723), 50 characters Matsunaga Ryōhitsu (1739)).
Following the Chinese tradition, Wasan books differ significantly in structure and style from contemporary Western mathematics books; they are organized according to specific problems that are explained separately. They are not structured according to a theoretical superstructure and do not have the Euclidean- oriented definition-sentence-proof scheme based on axioms . Another typical feature of Wasan books is the Idai ( 遺 題 ). At the end of the book, unsolved problems are formulated here, which other mathematicians can take up and work on.
Another phenomenon of the Wasan period was the Sangaku ( Japanese 算 額 , literally "mathematical table / tablet"). These were wooden panels on which geometric puzzles were described. These were hung on temples as an offering or for the intellectual challenge of pilgrims. Sangaku was practiced not only by scholars but by all social classes.
From 1868 Wasan was replaced by Western mathematics ( yōsan ) as part of the reforms of the Meiji government .
Important 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 (1732–1798)
- Aida Yasuaki (1747-1817)
- Sakabe Kōhan (1759-1824)
- Hasegawa Hiroshi (1782 / 83-1838)
- Wada Yasushi (1787-1840)
- Shiraishi Nagatada (1796–1862)
- Koide Shuki (1797-1865)
- Omura Isshu (1824-1871)
- Sato Seiko
See also
literature
- Annick Horiuchi : Japanese Mathematics in the Edo Period (1600–1868) , Birkhäuser 2010
- Yoshio Mikami : The development of mathematics in China and Japan (= Treatises on the history of the mathematical sciences including their applications. Vol. 30, ZDB -ID 531922-5 ). Teubner et al., Leipzig et al. 1913 (Reprint, 2nd edition. With an appendix on Soroban calculation by R. Fujisawa. Chelsea, New York NY 1974, ISBN 0-8284-0149-7 ).
- David Eugene Smith , Yoshio Mikami: A History of Japanese Mathematics. The Open Court Publishing Company, Chicago IL 1914, full online copy at archive.org , (Unabridged. Dover Publications Inc., Mineola NY Y 2004, ISBN 0-486-43482-6 ).
- CJ Scriba , Peter Schreiber: 5000 years of geometry. History, cultures, people. 3. Edition. Springer Heidelberg et al. 2010, ISBN 978-3-642-02361-3 , pp. 129ff. ( Excerpt (Google) ).
- Harald Kümmerle: Bibliography on traditional mathematics in Japan (wasan) .
Web links
- Morimoto, Mitsuo: A Chinese Root of Japanese Traditional Mathematics - Wasan