Japanese mathematics ( 和算 , wasan ) denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term wasan , from wa ("Japanese") and san ("calculation"), was coined in the 1870s and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 yōsan ).
12-508: Jinkōki ( 塵劫記 , じんこうき, Permanent Mathematics ) is a three-volume work on Japanese mathematics , first edited and published by Yoshida Mitsuyoshi in 1627. Over his lifetime, Mitsuyoshi revised Jinkōki several times. The edition released in the eleventh year of the Kan'ei era (1641) became particularly widespread. The last version personally published by Mitsuyoshi was the Idai ( 井大 ), which came out in
24-596: A new generation of mathematicians, and redefined the Japanese perception of educational enlightenment, which was defined in the Seventeen Article Constitution as "the product of earnest meditation". Seki Takakazu founded enri (円理: circle principles), a mathematical system with the same purpose as calculus at a similar time to calculus's development in Europe. However Seki's investigations did not proceed from
36-474: Is a characteristic of the book that explanations are given using familiar topics, such as using the increase of mice as an example for geometric progression . Many different versions were published, with slightly modified content, and by the time of the Meiji era , over 400 editions of Jinkōki had been published. Japanese mathematics In the history of mathematics , the development of wasan falls outside
48-578: Is derived from jintenkō ( 塵点劫 ), an immeasurably long span of time mentioned in the Lotus Sutra , hence the nuance of permanence in the Sino-Japanese word jinkō and its reflection in English title. The book contained instructions for dividing and multiplying with a soroban and mathematical problems relevant to merchants and craftsmen. The book also contained several interesting mathematical problems, and
60-503: Is suggested that this period saw the use of an exponential numbering system following the law of a m ∗ a n = a m + n {\displaystyle a^{m}*a^{n}=a^{m+n}} . The Japanese mathematical schema evolved during a period when Japan's people were isolated from European influences, but instead borrowed from ancient mathematical texts written in China, including those from
72-655: The Josephus problem . The Shinpen Jinkōki was the most widespread version among the copies of Jinkōki, and widely used as a textbook for use of the soroban throughout the Edo period. In addition to fundamental knowledge such as numerical notation, units, and multiplication tables, it also included slightly more specialised topics, such as methods to find square roots and cube roots , practical calculations of area, currency conversion , and interest calculation . The content covers almost all arithmetic needed in daily life at that time, and it
84-617: The Yuan dynasty and earlier. The Japanese mathematicians Yoshida Shichibei Kōyū , Imamura Chishō , and Takahara Kisshu are among the earliest known Japanese mathematicians. They came to be known to their contemporaries as "the Three Arithmeticians". Yoshida was the author of the oldest extant Japanese mathematical text, the 1627 work called Jinkōki . The work dealt with the subject of soroban arithmetic , including square and cube root operations. Yoshida's book significantly inspired
96-683: The Western realm. At the beginning of the Meiji period (1868–1912), Japan and its people opened themselves to the West. Japanese scholars adopted Western mathematical technique, and this led to a decline of interest in the ideas used in wasan . Records of mathematics in the early periods of Japanese history are nearly nonexistent. Though it was at this time that a large influx of knowledge from China reached Japan , including that of reading and writing , little sources exist of usage of mathematics within Japan. However, it
108-491: The eighteenth year of the Kan'ei (1634). Subsequent to that, various editions of Jinkōki were released, one of which includes Shinpen Jinkōki ( 新編塵劫記 ). Jinkōki is one of the most popular and influential Japanese mathematics books in history, having influenced Seki Takakazu , Kaibara Ekken , and many other later Japanese mathematicians. It is partly based on the works of Yuan dynasty mathematicians in China. The name Jinkōki
120-700: The same foundations as those used in Newton's studies in Europe. Mathematicians like Takebe Katahiro played an important role in developing Enri (" circle principle"), a crude analog to the Western calculus. He obtained power series expansion of ( arcsin ( x ) ) 2 {\displaystyle (\arcsin(x))^{2}} in 1722, 15 years earlier than Euler . He used Richardson extrapolation in 1695, about 200 years earlier than Richardson. He also computed 41 digits of π, based on polygon approximation and Richardson extrapolation. The following list encompasses mathematicians whose work
132-417: The soroban. The second and third volumes include an assortment of practical and recreational problems. The included problems are not arranged according to any specific order. The book includes ideas that aimed to keep readers from boredom by adopting a wide variety of problems such as calculations of areas of rice fields, problems related to the construction of rivers and riverbanks, geometric progression, and
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#1732858980753144-501: Was the first Japanese book to use printing in colour . As a result, the Jinkōki became the most popular Japanese mathematics book ever and one of the most widely read books of the Edo period . Mitsuyoshi made reference to everyday problems, such as buying and selling rice . The book was originally published in three volumes, the first of which mainly describes multiplication and division using
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