Seki Takakazu
From Wikipedia, the free encyclopedia
Seki Takakazu (関 孝和 Seki Takakazu?) (born 1637 or 1642? – October 24, 1708) was a Japanese mathematician who created a new mathematical notation system and used it to discover many of the theorems and theories that were being—or were shortly to be—discovered in the West, including recreating some results in calculus. He was a contemporary with Gottfried Leibniz and Isaac Newton, although he is not known to have had contact with them. It is said he discovered Bernoulli numbers before Jacob Bernoulli.
Much of his reputation stems from the formation of a school of mathematicians, called Seki school, which had been the most influential in Japan until the end of Edo period.
Seki was born in Fujioka in Gunma prefecture to the Uchiyama clan, and was later adopted into the Seki family. His birth year is disputed; since the Meiji period there have been two theories—one that he was born in 1637, and another that it was 1642. Neither theory is backed up by conclusive evidence.[1]
He introduced kanji to represent unknowns and variables in equations, although he was obliged to confine his work to equations up to the fifth degree—his algebraic alphabet (endan-jutsu) was not suitable for general equations of the nth degree. He was able to create equations with literal coefficients of any degree and with several variables, and to solve simultaneous equations. In this way he was able to derive the equivalent of f(x), and thereby to arrive at the notion of a discriminant—a special function of the root of an equation expressible in terms of the coefficients.
A notable Seki's contribution to algebra is the discovery of determinants. He treated only 2x2 and 3x3 matrices, and failed to obtain general formula. Yet his result was more general than the one obtained by Leibniz ten years later. The general case was successfully treated by his students, who discovered Laplace's formula, earlier than Laplace. They used determinant to eliminate variables in simultaneous equations.
Another of Seki's contributions was the rectification of the circle, i.e. the calculation of pi; he obtained a value for π that was correct to the 10th decimal place, using Aitken's delta-squared process, which was rediscovered in the 20th century by Aitken.
[edit] References
- ^ Fujiwara, Masahiko (2002). Tensai no Eikō to Zasetsu. Shinchosha.
[edit] External links
- O'Connor, John J., and Edmund F. Robertson. "Seki Takakazu". MacTutor History of Mathematics archive.
