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).
In the history of mathematics, the development of wasan falls outside the Western realms of people, propositions and alternate solutions.[ clarification needed ] 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.
This mathematical schema evolved during a period when Japan's people were isolated from European influences. Kambei Mori is the first Japanese mathematician noted in history.Kambei is known as a teacher of Japanese mathematics; and among his most prominent students were Yoshida Shichibei Kōyū, Imamura Chishō, and Takahara Kisshu. These students 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 was named Jinkōki. The work dealt with the subject of soroban arithmetic, 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 at a similar time to calculus's development in Europe; but Seki's investigations did not proceed from conventionally shared foundations[ clarification needed ].
The following list encompasses mathematicians whose work was derived from wasan.
Seki Takakazu, also known as Seki Kōwa, was a Japanese mathematician and author of the Edo period.
Shigefumi Mori is a Japanese mathematician, known for his work in algebraic geometry, particularly in relation to the classification of three-folds.
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 ShigeyoshiMōri 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.
Miquel's theorem is a result in geometry, named after Auguste Miquel, concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles in Euclidean geometry due to Miquel, whose work was published in Liouville's newly founded journal Journal de mathématiques pures et appliquées.
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.
Muramatsu Shigekiyo was a Japanese mathematician and curator in the Edo period. He is known for being the first to calculate the volume of a sphere using very thin slices, and to use inscribed and circumscribed polygones to approximate the circumference of a circle, and hence π. And by using a 32768-gon, he calculated its perimeter as 3.141592648... He published his value of π to 22 decimal places in his 1663 book Sanso, but only 8 were correct. Later, in 1681, Seki Takakazu used the same method with a 131072-gon, and got π correct to 11 decimal places.
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).
Sacred Mathematics: Japanese Temple Geometry is a book on Sangaku, geometry problems presented on wooden tablets as temple offerings in the Edo period of Japan. It was written by Fukagawa Hidetoshi and Tony Rothman, and published in 2008 by the Princeton University Press. It won the PROSE Award of the Association of American Publishers in 2008 as the best book in mathematics for that year.