**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^{ [1] } and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 *yōsan*).^{ [2] }

- History
- Pre-Edo period (552-1600)
- Edo period
- Select mathematicians
- See also
- Notes
- References
- External links

In the history of mathematics, the development of *wasan* falls outside 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 is suggested that this period saw the use of an exponential numbering system following the law of .^{ [3] }

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 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".^{ [4] }^{ [5] }

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.^{ [6] } Yoshida's book significantly inspired 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".^{ [7] }

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 the same foundations as those used in Newton's studies in Europe.^{ [8] }

Mathematicians like Takebe Katahiro played an important role in developing Enri (" circle principle"), a crude analog to the Western calculus.^{ [9] } He obtained power series expansion of in 1722, 15 years earlier than Euler. He used Richardson extrapolation in 1695, about 200 years earlier than Richardson.^{ [10] } He also computed 41 digits of π, based on polygon approximation and Richardson extrapolation.^{ [11] }

The following list encompasses mathematicians whose work was derived from *wasan.*

- Yoshida Mitsuyoshi (1598–1672)
- Seki Takakazu (1642–1708)
- Takebe Kenkō (1664–1739)
- Matsunaga Ryohitsu (fl. 1718-1749)
^{ [12] } - Kurushima Kinai (d. 1757)
- Arima Raido (1714–1783)
^{ [13] } - Fujita Sadasuke (1734-1807)
^{ [14] } - Ajima Naonobu (1739–1783)
- Aida Yasuaki (1747–1817)
- Sakabe Kōhan (1759–1824)
- Fujita Kagen (1765–1821)
^{ [14] } - Hasegawa Ken (c. 1783-1838)
^{ [13] } - Wada Nei (1787–1840)
- Shiraishi Chochu (1796–1862)
^{ [15] } - Koide Shuke (1797–1865)
^{ [13] } - Omura Isshu (1824–1871)
^{ [13] }

- Japanese theorem for cyclic polygons
- Japanese theorem for cyclic quadrilaterals
- Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in Shinto shrines
- Soroban, a Japanese abacus
- Category:Japanese mathematicians

- ↑ Selin, Helaine. (1997).
*Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures*, p. 641. - ↑ Smith, David
*et al.*(1914).*A History of Japanese Mathematics*, p. 1 n2. - ↑ Smith,
*pp. 1–6.*, p. 1, at Google Books - ↑ Smith,
*p. 35.*, p. 35, at Google Books - ↑ Campbell, Douglas
*et al.*(1984).*Mathematics: People, Problems, Results,*p. 48. - ↑ Restivo, Sal P. (1984).
*Mathematics in Society and History*, p. 56. - ↑ Strayer, Robert (2000).
*Ways of the World: A Brief Global History with Sources*. Bedford/St. Martins. p. 7. ISBN 9780312489168. OCLC 708036979. - ↑ Smith,
*pp. 91–127.*, p. 91, at Google Books - ↑ Mathematical Society of Japan, Takebe Prize
- ↑ Osada, Naoki (Aug 26, 2011). "収束の加速法の歴史 : 17世紀ヨーロッパと日本の加速法 (数学史の研究)" (PDF).
*Study of the History of Mathematics RIMS Kôkyûroku*(in Japanese).**1787**: 100–102 – via Kyoto University. - ↑ Ogawa, Tsugane (May 13, 1997). "円理の萌芽 : 建部賢弘の円周率計算 : (数学史の研究)" (PDF).
*Study of the History of Mathematics RIMS Kôkyûroku*(in Japanese).**1019**: 80–88 – via Kyoto University. - ↑ Smith,
*pp. 104, 158, 180.*, p. 104, at Google Books - 1 2 3 4 List of Japanese mathematicians -- Clark University, Dept. of Mathematics and Computer Science
- 1 2 Fukagawa, Hidetoshi
*et al.*(2008).*Sacred Mathematics: Japanese Temple Geometry*, p. 24. - ↑ Smith,
*p. 233.*, p. 233, at Google Books

**Seki Takakazu**, also known as **Seki Kōwa**, was a Japanese mathematician and author of the Edo period.

**Ajima Naonobu**, also known as **Ajima Manzō Chokuyen**, was a Japanese mathematician of the Edo period.

**Sangaku** or **san gaku** are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples during the Edo period by members of all social classes.

**Aida Yasuaki** also known as **Aida Ammei**, was a Japanese mathematician in the Edo period.

**Dan Pedoe** was an English-born mathematician and geometer with a career spanning more than sixty years. In the course of his life he wrote approximately fifty research and expository papers in geometry. He is also the author of various core books on mathematics and geometry some of which have remained in print for decades and been translated into several languages. These books include the three-volume *Methods of Algebraic Geometry*, *The Gentle Art of Mathematics*, *Circles: A Mathematical View*, *Geometry and the Visual Arts* and most recently *Japanese Temple Geometry Problems: San Gaku*.

In geometry, **Soddy's hexlet** is a chain of six spheres, each of which is tangent to both of its neighbors and also to three mutually tangent given spheres. In Figure 1, the three spheres are the red inner sphere and two spheres above and below the plane the centers of the hexlet spheres lie on. In addition, the hexlet spheres are tangent to a fourth sphere, which is not tangent to the three others.

**Takebe Katahiro**, also known as **Takebe Kenkō**, was a Japanese mathematician and cartographer during the Edo period.

**Wada Yenzō Nei**, also known as **Wada Yasushi**, was a Japanese mathematician in the Edo period. His birth name was Kōyama Naoaki; but he changed his name to Wada Nei, by which he became more widely known.

**Kambei Mori** or **Mōri Kambei**, also known as **Mōri Kambei Shigeyoshi****Mōri Shigeyoshi**, was a Japanese mathematician in the Edo period.

**Yoshida Mitsuyoshi**, also known as **Yoshida Kōyū**, was a Japanese mathematician in the Edo period. His popular and widely disseminated published work made him the most well known writer about mathematics in his lifetime.

**Yoshio Mikami** was a Japanese mathematician and historian of *Japanese mathematics*. He was born February 16, 1875, in Kotachi, Hiroshima prefecture. He attended the High School of Tohoku University, and in 1911 was admitted to the Imperial University of Tokyo. He studied history of Japanese and Chinese mathematics. In 1913, he published "The Development of Mathematics in China and Japan" in Leipzig. This book consisted of two parts with 47 chapters. Part one has 21 chapters that describe in depth several important Chinese mathematicians and mathematical classics including Liu Hui, Shen Kuo, Qin Jiushao, Sun Tzu, The Nine Chapters on the Mathematical Art, Mathematical Treatise in Nine Sections, Li Ye, Zhu Shijie and study on π. Part II deals with important *wasan* mathematicians and their works, including Kambei Mori, Yoshida Koyu, Kowa Seki, Imamura Chisho, Takahara Kisshu, Kurushima, Ajima Chokuyen, Aida Ammei, Shiraishi Chochu, Skabe Kohan, and Hagiwara Teisuke.

The **Mathematical Society of Japan** is a learned society for mathematics in Japan.

**Sakabe Kōhan** was a Japanese mathematician in the Edo period.

**Kurushima Kinai**, also known as **Kurushima Yoshita** and **Kurushima Yoshihiro**, was a Japanese mathematician in the Edo period.

**Koide Chōjūrō**, also known as **Koide Shuke**, was a Japanese mathematician in the Edo period.

**Fujita Sadasuke**, also known as Honda Teiken, was a Japanese mathematician in the Edo period. He is the author of *Seiyō sampō* which was published in 1781.

**Akio Hattori** was a Japanese mathematician working in algebraic topology who proved the Hattori–Stong theorem. Hattori was the president of the Mathematical Society of Japan in 1989–1991.

**Annick Mito Horiuchi** is a French historian of mathematics and historian of science. She is a professor at Paris Diderot University, where she is associated with the Centre de recherche sur les civilisations de l'Asie orientale (CRCAO).

**Jinkōki** 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 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).

**Yamaji Nuchizumi**, was a Japanese mathematician in the middle of the Edo period, focused on calendar reform.

- Campbell, Douglas M. and John C. Iggins. (1984).
*Mathematics: People, Problems, Results.*Belmont, California: Warsworth International. ISBN 9780534032005; ISBN 9780534032012; ISBN 9780534028794; OCLC 300429874 - Endō Toshisada (1896).
*History of mathematics in Japan*(日本數學史,*Dai Nihon sūgakush*). Tōkyō: _____. OCLC 122770600 - Fukagawa, Hidetoshi, and Dan Pedoe. (1989).
*Japanese temple geometry problems = Sangaku*. Winnipeg: Charles Babbage. ISBN 9780919611214; OCLC 474564475 - __________ and Dan Pedoe. (1991)
*How to resolve Japanese temple geometry problems?*(日本の幾何ー何題解けますか?,*Nihon no kika nan dai tokemasu ka*) Tōkyō. ISBN 9784627015302; OCLC 47500620 - __________ and Tony Rothman. (2008).
*Sacred Mathematics: Japanese Temple Geometry*. Princeton: Princeton University Press. ISBN 069112745X; OCLC 181142099 - Horiuchi, Annick. (1994).
*Les Mathematiques Japonaises a L'Epoque d'Edo (1600–1868): Une Etude des Travaux de Seki Takakazu (?-1708) et de Takebe Katahiro (1664–1739).*Paris: Librairie Philosophique J. Vrin. ISBN 9782711612130; OCLC 318334322 - __________. (1998). "Les mathématiques peuvent-elles n'être que pur divertissement? Une analyse des tablettes votives de mathématiques à l'époque d'Edo."
*Extrême-Orient, Extrême-Occident*, volume 20, pp. 135–156. - Kobayashi, Tatsuhiko. (2002) "What kind of mathematics and terminology was transmitted into 18th-century Japan from China?",
*Historia Scientiarum*, Vol.12, No.1. - Kobayashi, Tatsuhiko. Trigonometry and Its Acceptance in the 18th-19th Centuries Japan.
- Ogawa, Tsukane. "A Review of the History of Japanese Mathematics".
*Revue d'histoire des mathématiques***7**, fascicule 1 (2001), 137-155. - Restivo, Sal P. (1992).
*Mathematics in Society and History: Sociological Inquiries.*Dordrecht: Kluwer Academic Publishers. ISBN 9780792317654; OCLC 25709270 - Selin, Helaine. (1997).
*Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures.*Dordrecht: Kluwer/Springer. ISBN 9780792340669; OCLC 186451909 - David Eugene Smith and Yoshio Mikami. (1914).
*A History of Japanese Mathematics.*Chicago: Open Court Publishing. OCLC 1515528;*see*online, multi-formatted, full-text book at archive.org

- Japan Academy, Collection of native Japanese mathematics
- JapanMath, Math program focused on Math Fact Fluency and Japanese originated logic games
- Sangaku
- Sansu Math, translated Tokyo Shoseki Japanese math curriculum
- Kümmerle, Harald.
*Bibliography on traditional mathematics in Japan (wasan)*

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