Takakazu seki biography

He wrote on magic squares , again in his work of , having studied a Chinese work by Yank Hui on the topic in This was the first treatment of the topic in Japan. He discovered the Newton or Newton - Raphson method for solving equations and also had a version of the Newton interpolation formula. Among other problems studied by Seki were Diophantine equations.

Secrecy surrounded the schools in Japan so it is hard to determine the contributions made by Seki, but he is also credited with major discoveries in the calculus which he passed on to his pupils. References show. Biography in Encyclopaedia Britannica. In addition to that, he amassed Chinese and Japanese textbooks with which he educated students like Takebe Kenko in maths and astronomy.

Alongside various commemoratives, the kilometer-wide Sekitakakazu asteroid is named in his honor. Thanks for this intro. It is the first time I am hearing about Seki Kowa Takakazu, and you made it both easy and interesting. With elimination theory in hand, a large part of the problems treated in Seki's time became solvable in principle, given the Chinese tradition of geometry almost reduced to algebra.

In practice, of course, the method could flounder under huge computational complexity. Yet this theory had a significant influence on the direction of development of wasan. After the elimination is done, one has to find the real roots of a single variable equation numerically. Horner's method, though completely known in China, was not transmitted to Japan in its final form.

So Seki had to work it out by himself independently—he is sometimes credited with Horner's method, which is not historically correct. He also suggested an improvement to Horner's method: to omit higher order terms after some iterations. This happens to be the same as the Newton-Raphson method, but in a completely different perspective. Neither he nor his pupils had the idea of derivative, strictly speaking.

He also studied the properties of algebraic equations, in the aim of assisting numerical work. The most notable of these are the conditions for the existence of multiple roots based on the discriminant, which is the resultant of a polynomial and its 'derivative': his working definition of 'derivative' is. Another of Seki's contributions was the rectification of the circle, i.

Seki's published writings encompass 52 works in 56 publications in 3 languages and library holdings. This is an incomplete list, which may never be able to satisfy particular standards for completeness. You can help by expanding it with reliably sourced entries. OCLC , collected works. Mathematics in Society and History: Sociological Inquiries, p.

Linear algebra: a Modern Introduction, p. From an early age, Seki Kowa showed himself a mathematical prodigy, earning the nickname "divine child" because of his remarkable abilities. At some point Seki Kowa married, though he never had any children, and went to work as an examiner of accounts for the Lord of Koshu. The latter eventually became shogun, and thus Seki Kowa—a member of the samurai class by birth—was named a shogunate samurai.

His work as an accountant, a trade he must have learned from his adoptive father, naturally dovetailed with his interests as a mathematician, and during his late twenties, he began to teach and write on the subject.

Takakazu seki biography

Seki Kowa's one notable publication was Hatubi sanpo, which appeared in The book was written in response to the announcement of some 15 supposedly unsolvable problems that had been put forth four years before; in Hatubi sanpo, Seki Kowa solved them all. However, it was not the Japanese custom to show how one had arrived at one's solutions, and it appears that even Seki Kowa's students remained unaware of his methodology.

Much of what the Japanese knew about mathematics had been derived as had many other aspects of their civilization from older Chinese models. Chinese math at the time made it possible to solve equations with a single variable, but Seki Kowa took this several steps further. In the course of his work, he implemented notation he had created to express these unknown quantities.

His work was all the more remarkable in light of the fact that Japanese mathematicians were unaware of algebra. It was Seki Kowa's achievement, however, to provide a number of advancements without the benefit of input from other scholars, a situation quite unlike that of his counterparts in Europe. Like Sir Isaac Newton , who was born the same year as he, he developed a method for approximating the root of a numerical equation, and he created his own table of determinants at about the same time this idea made its debut in Europe.

In his latter years, Seki Kowa was granted the title of master of ceremonies for the shogun's household, an esteemed position.