denotes a distinct kind of mathematics which was developed in

Japan Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the n ...

during the

Edo period The or is the period between 1603 and 1867 in the history of Japan, when Japan was under the rule of the Tokugawa shogunate and the country's 300 regional '' daimyo''. Emerging from the chaos of the Sengoku period, the Edo period was character ...

(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''). In the

history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

, the development of ''wasan'' falls outside the Western realm. At the beginning of the

Meiji period The is an era of Japanese history that extended from October 23, 1868 to July 30, 1912. The Meiji era was the first half of the Empire of Japan, when the Japanese people moved from being an isolated feudal society at risk of colonization ...

(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''.

History

The Japanese mathematical

schema The word schema comes from the Greek word ('), which means ''shape'', or more generally, ''plan''. The plural is ('). In English, both ''schemas'' and ''schemata'' are used as plural forms. Schema may refer to: Science and technology * 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 The Yuan dynasty (), officially the Great Yuan (; xng, , , literally "Great Yuan State"), was a Mongol-led imperial dynasty of China and a successor state to the Mongol Empire after its division. It was established by Kublai, the fif ...

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".Smith, Yoshida was the author of the oldest extant Japanese mathematical text, the 1627 work called ''Jinkōki''. The work dealt with the subject of

soroban The is an abacus developed in Japan. It is derived from the ancient Chinese suanpan, imported to Japan in the 14th century. Like the suanpan, the soroban is still used today, despite the proliferation of practical and affordable pocket electr ...

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

, including square and cube root operations. 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". Seki Takakazu founded ''enri'' (円理: circle principles), a mathematical system with the same purpose as

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

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. Mathematicans like Takebe Katahiro played and important role in developing Enri (" circle principle"), a crude analog to the Western calculus. Mathematical Society of Japan
/ref> He obtained

power series In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''an'' represents the coefficient of the ''n''th term and ''c'' is a con ...

expansion of

(arcsin(x))^2

in 1722, 15 years earlier than

Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ...

. He used

Richardson extrapolation In numerical analysis, Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value A^\ast = \lim_ A(h). In essence, given the value of A(h) for several values of h, ...

in 1695, about 200 years earlier than Richardson. He also computed 41 digits of π, based on polygon approximation and Richardson extrapolation.

Select mathematicians

Seki Kowa Katsuyo Sampo Bernoulli numbers

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. ''Floruit'' (; abbreviated fl. or occasionally flor.; from Latin for "they flourished") denotes a date or period during which a person was known to have been alive or active. In English, the unabbreviated word may also be used as a noun indicatin ...

1718-1749) * Kurushima Kinai (d. 1757) * Arima Raido (1714–1783) List of Japanese mathematicians
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Clark University Clark University is a private research university in Worcester, Massachusetts. Founded in 1887 with a large endowment from its namesake Jonas Gilman Clark, a prominent businessman, Clark was one of the first modern research universities in th ...