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Yoshida Mitsuyoshi (Japanese 吉田 光由; born 1598; died 1672), or Yoshida Kōyū in Sino-Japanese lection, was a Japanese mathematician from the Edo period. He wrote the widespreed publisherd arithmetic book Jinkōki (塵劫記), which became highly influential for future authors and was teached in several math classes. Together with Imamura Chishō and Takahara Kisshu he belongs to "The three Arithmeticians".[1]

Life

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Yoshida was born in Saga, a suburb of Kyōto, to a physician. His relationship to the rich merchant family Suminokura enabled him an extensive education and gave the mathematically gifted Yoshida access to Chinese math books, such as the 1592 book Sanpō Tōsō (Chinese: 算法统宗; pinyin: Suànfă tŏngzóng), on which he later drew on at his own works.[2] Because of his skills he was elected a pupil for Mōri Kambei Shigeyoshi from the family of daimyō, Mōri, who wrote the first recorded math books in native Japanese, but which were yet not found.[1]

Yoshida calculated with the Japanese abacus soroban.

The economic boom after the time of troubles in the Azuchi–Momoyama period and the reunion of the country under the Tokugawa shogunate was accompanied by an increased demand for mathematical calculations, which, however, were exacerbated through imperfect algorithm and a complicated currency system. Constant conversions were needed between Edo's Gold standards, Kyōto's and Ōsaka's Silver standards and different Copper standards, as well as the various masses and weights. The Japanese abacus, the soroban, was a helpful tool to calculate such calculations. The tool was rarely used in calculations and in the most important arithmetic techniques.

Yoshida tried to bridge the gap with the arithmetic book Jinkōki issued in 1627, similar to Adam Riese one century ago with the first math book. The book included apart from daily required mathematical algorithms numerous teasers, for which Yoshida partially drew on Chinese models, such as the Sanpō Tōsō. He reworked his work several times until the end of 1641 and tried to rival with numerous imitators through innovations such as coloured illustrations, different colours for positive (red) and negative integers (black) and finally the so-called idai shōtō, "mathematical problems proposed for solution and solved in subsequent works", a collection of twelve unresolved tasks. The book also gives value of 3.16 for π.[3]

After 1641, Yoshida turned towards river engineering projects. It is disputed whether he wrote a 1643 book which is attributed to him, but it is reasonably certain that he was involved in two calendric works, the Wakan Hennen Gōunzen (1645) and the Koreki Binran (1648). Yoshida Mitsuyoshi died in 1672.

Werk

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Representation of the binomial coefficients in Jinkōki, 1641

Yoshida's most famous work, the Jinkōki, was released between 1627 and 1641 in at least six partly very different editions. The book was used until the European-oriented school reforms in the early Meiji period in Terakoya schools. The Jinkōki is among the most widely used books in the traditional Japanese arithmetic (和算, Wasan), which was, unlike the more scientific-oriented math for experts, such as the seki schoo (named after Seki Takakazu) and the culuturally significant Sangaku boards, intended more for the domestic use. The drawings possibly created by the author contributed to the practical use of the work. He relinquished to use mathematical notations, and all tasks are described with words and with regard to calculations with the soroban.

The editions of Jinkōki are:

  • 1627: Everyday calculations and the surface and volume are described on four issues with 26 chapters.
  • 1629: Additionally to the first edition, this version comprises in five issues and 48 chapters the calculations with large numbers and some tasks with game theory character.
  • 1631: Die drei Bände mit insgesamt ebenfalls 48 Kapiteln enthalten zum Schutz vor Nachahmern farbige Illustrationen und farbig gekennzeichnete positive und negative Zahlen.
  • 1634: Diese Ausgabe besteht aus vier kleinformatigen Bänden mit insgesamt wiederum 48 Kapiteln, unterscheidet sich jedoch inhaltlich deutlich von den vorherigen und späteren Ausgaben.
  • Juni 1641: In drei Bänden mit insgesamt 50 Kapiteln werden die Inhalte der bisherigen Ausgaben umfassend und weitgehend in sich geschlossen dargestellt. Der erste Band enthält eine Einführung in das Soroban-Rechnen sowie Aufgaben zu Reispreisen, Geldwechsel, Zinsrechnung und Wareneinkauf. Im zweiten Band finden sich Aufgaben, die für einzelne Berufsgruppen wie Händler, Bauern, Handwerker oder Landaufseher von besonderem Interesse sind, etwa die Berechnung der Fläche von Reisfeldern oder der Getreidesteuer. Der dritte Band besteht aus Aufgaben, die dazu geeignet sind, mathematische Laien zu beeindrucken, wie exponentielles Wachstum, Quadrat- und Kubikwurzeln.
  • November 1641: Diese möglicherweise als Supplementband zur Ausgabe vom Juni desselben Jahres gedachte Ausgabe enthält neben weiteren Aufgaben zu Oberflächen und Volumina fester Körper auch die zwölf „noch zu lösenden Probleme“.

Yoshidas Buch war nur eines von vielen Rechenbüchern, die in der ersten Hälfte des 17. Jahrhunderts in Japan entstanden. Es gewann jedoch offensichtlich großen Einfluss sowohl auf nachfolgende Autoren, die sein Verfasser nach eigenem Bekunden als Nachahmer und Schwarzkopierer betrachtete, als auch auf den Mathematikunterricht. Noch hundert Jahre nach Yoshidas Tod erschien kaum ein Buch ohne „noch zu lösende Probleme“, deren Anzahl zum Teil bis zu 200 betrug. Bis 1913 wurden über 300 Rechenbücher veröffentlicht, die den Begriff Jinkōki im Namen trugen. Erst mit den Schulreformen der Meiji-Zeit ab 1872 und der damit verbundenen Bevorzugung westlicher Mathematik (Yosan) verlor Yoshida an Bedeutung. Durch Neuausgaben seines Werks in englischer und moderner japanischer Sprache wurde er seit Ende der 1990er Jahre wieder bekannter.

Ausgaben

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  • Osamu Takenouchi u. a. (2000). Jinkōki. Tokyo: Wasan Institute. {{cite book}}: Unknown parameter |comment= ignored (help)

References

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  1. ^ a b Smith & Mikami 1914, p. 35.
  2. ^ Smith & Mikami 1914, p. 59-60.
  3. ^ Smith & Mikami 1914, p. 60-61.
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