Seki Takakazu

Takakazu Seki (Japanese关 孝 和; * 1637/1642 in Fujioka, † December 5, 1708; Traditional Date: 10/05/24 Hui ), Seki Kowa also ( the Sino- Japanese reading of his name ), was a Japanese mathematician. He discovered many theorems and theories that have been previously or only afterwards discovered shortly independently in Europe, and is considered the most important mathematicians of the Wasan.

Life

For his studies Seki Takakazu resorted to then largely unknown Chinese works from the Song and Yuan Dynasties substantially. He was a vassal of daimyo of the Tokugawa feudal Kōfu Tsunashige and his son Tokugawa Tsunatoyo, the later Tokugawa shogun 6.

His reputation stems mainly from the justified by his works Seki school, which was the most influential in Japan until the end of the Edo period.

In his 1685 published work Kaiindai no Hō (解 伏 题 之 法, dt " method to solve hidden problems " ) he describes an ancient Chinese method for calculating the zeros of polynomials and extends them by finding all the real zeros. He also discovered the Bernoulli numbers before Bernoulli.

He played an important part in the discovery of determinants. Although he treated only 2 × 2 - and 3 × 3 matrices and not managed to extend the calculation to the general case, but was more general than Leibniz 10 years later. The general case was treated by his students who developed the Laplace expansion theorem before Laplace. They used determinants in order to eliminate variables in the equation system.

In the calculation of the circular area, and thus the circuit in contrast to the number it used in Europe used exhaustion based on the Einbeschreibung a finite number of polygons, an infinite series. The series used in Europe until 1737 appeared to in a letter from Euler to Johann Bernoulli. This method to solve quadratic equations by infinite series is called Enri (円 理, dt "circle principle").