Takebe Katahiro

Takebe Katahiro ( Japanese 建 部 賢 弘 ; * 1664 in Edo , Japan ; † August 24, 1739 ibid), also Takebe Kenkō (the Sino-Japanese reading of his name), was a Japanese mathematician of Wasan and a student of Seki Takakazu .

His older brother Takebe Kataaki (1661-1716) was also a mathematician and a student of Seki.

Takebe was a student of Seki from the age of thirteen and stayed with him (like his brother) until his death in 1708. The brothers were able to use the extensive library of Seki and spread and popularized his work and defended it against falsification. They were instrumental in Seki's project to publish a series of 20 books of mathematical classics (Taisei sankei), which began in 1683 and was completed by Takebe's brother in 1710. The work came from Takebe in the first twelve volumes and from his brother in the last eight.

Since Seki was a samurai and later in a high position with the Shogun Tokugawa Ienobu, Takebe also lived in these circles (from around 1695) and had less and less time for mathematics. He served various members of the Tokugawa family, such as Tokugawa Ienobu, who became a shogun in 1709, and his successor (from 1712) as Shogun Tokugawa Ietsugu and Tokugawa Yoshimune (Shogun from 1716). The latter was also interested in mathematics and astronomy, so Takebe devoted himself more to these areas. The Shogun also relaxed the import ban on foreign books, especially scientific books from the West, and had a globe and a telescope made. In the 1720s, Takebe was primarily concerned with astronomy and calendar issues.

In his first two books (Kenki Sanpo 1683, Hatsupi Sanpo Endan Genkai 1685) he expanded the treatment of polynomials by Seki, but it was also based on his study of the Chinese classic Suanxue qimeng by Zhu Shijie , which he also commented on in 1690 in Japanese translation issued. The book Hatsupi Sanpo Endan Genkai was an explanation of the methods of his teacher Seki which had led him to solve the problems in his book Hatsupi Sanpo. As is customary in the Seki school, not everything is communicated, but important parts are only passed on within the school (some of which were only published in the 20th century). Takebe's most important work was Tetsujutsu Sankei from 1722, in which he presented important results and methods of the Seki school such as the expansion of the Chinese representation of algebraic equations by Zhu Shijie to include several variables, his arcsin series and his calculation of pi.

He developed the Enri ( 円 理 , dt. "Circle principle") (the school's method to find good approximations in problems such as determining the circumference of a circle by approximation using regular polygons). Among other things, he gave an infinite series for the square of the arcsine (first found in the west by Euler in 1737) and in 1723 calculated the number of circles to the nearest 41 digits using Richardson extrapolation (long before the method was rediscovered by Lewis Fry Richardson ) similar to in the Romberg integration . ${\displaystyle \pi }$

literature

• David Eugene Smith , Yoshio Mikami : A History of Japanese Mathematics . Open Court Publishing, Chicago 1914, p. 146ff ( full online version at archive.org )
• Annick Horiuchi: Japanese Mathematics in the Edo Period (1600-1868). A Study of the works of Seki Takakazu (? -1708) and Takebe Takahiro (1664-1739) . Birkhäuser, Basel 2010. ISBN 978-3447107747
• Eberhard Knobloch, Hikosaburo Komatsu, Dun Liu (Eds.): Seki, Founder of Modern Mathematics in Japan. A Commemoration of his Tercentenary , Springer 2013

Web links

• John J. O'Connor, Edmund F. Robertson :  Takebe Katahiro. In: MacTutor History of Mathematics archive .
• Takebe Katahiro Entry in the Encyclopedia britannica

Japanese name: As is common in Japan, the family name comes before the first name in this article . Thus Takebe is the family name, Katahiro the first name.