Seki Kōwa

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In this Japanese name, the family name is Seki.
Kōwa Seki (Takakazu Seki)
Kōwa Seki (Takakazu Seki)
Kōwa Seki (Takakazu Seki)
Born March(?), 1642(?)
Edo or Fujioka, Japan
Died December 5, 1708 (Gregorian calendar)
Japan
Residence Japan
Nationality Japanese
Fields Mathematician
Seki Takakazu
Seki Takakazu

Seki Kōwa (関孝和?) or Seki Takakazu (関孝和 Seki Takakazu?) (born 1637/1642? – 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 it is obvious that he could not have had contact with them. It is said[citation needed] he discovered Bernoulli numbers before Jacob Bernoulli.

Much of his reputation stems from the formation of a school of mathematicians, called Seki school, which was 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 opinions — one that he was born in 1637, and another that it was 1642. Neither opinion 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 contribution of Seki's to algebra is the discovery of determinants.[2] In his first manuscript(解伏題之法, Kai-fukudai-no-hou, 1683),he treated only 2x2, 3x3, and 4x4 matrices correctly, and his formula for 5x5 matrices was incorrect. Yet in in his later publication (大成算経 Taisei-sankei, written in 1683-1710), he presented correct and general formula (Laplace's formula). His first manuscript was as eary as Leibniz's first commentary on the subject, and the second one is almost half a century earlier than Laplace.

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 what is now called "Aitken's delta-squared process," rediscovered in the 20th century by Alexander Aitken.

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[edit] References

  1. ^ Fujiwara, Masahiko (2002). Tensai no Eikō to Zasetsu. Shinchosha. 
  2. ^ Howard Eves: "An Introduction to the History of Mathematics", page 405, Saunders College Publishing, 1990. (ISBN 0030295580)