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Seki - A Great Mathematician

For Algebra II

Alexa Hiznay

on 5 May 2010

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Transcript of Seki - A Great Mathematician

The Greatest Mathematicians of All Time Seki Takakazu was born c. 1640 in Fujioka, Japan
- died in 1708 in Edo, Japan

He was the second son of Nagaakira Uchiyama (a samuri)

Was adopted at an early age by Seki Gorōzaemon (an official with the Bureau of Supply in Edo)

Seki's early education is unkown, though it is suspected that he was self - educated after being introduced to mathematics by a servant at the age of nine years

Some of the writings that inspired Seki were:

- Zhu Shijie’s “Introduction to Mathematical Science"

- Yang Hui’s “Yang Hui’s Mathematical Methods”

- Cheng Dawei’s “Systematic Treatise on Arithmetic”
His early life STARRING:
SEKI Seki's achievements

Substituted a tabular notational system in place of the outdated Chinese method of using an abacus, which simplified the handling of equations with more than one unknown variable

Seki also perfected the extraction of roots (solutions) of higher-degree polynomial equations

In 1674 Seki solved fifteen algebra problems which had been posed four years earlier by Sawaguchi Kazuyuki in "Kokin-Sanpo-Ki"

- multi-variable equations were required, instead of the more simplistic arithmetical methods

Seki was the first person to study determinants in 1683

Calculated a value for pi that was correct to the 10th decimal place (using what is now called "Aitken's delta-squared process," which was rediscovered in the 1900s by Alexander Aitken)

A summation of Seki A child prodigy

Crucial in recovering forgotten mathematical knowledge from ancient Chinese mathematicians

Also worked on extending and generalizing the main problems

Focused mostly on algebra, a field in which he created effective new tools and provided definitive solutions

Anticipated the discoveries of several Western mathematicians As Seki once said, “Mathematics is more than an art form.”
Seki was known as "The Arithmetical Sage" Seki's Publications Seki had classified three types of problems: explicit problems, which can be solved by arithmetic, implicit problems, which can be solved by an algebraic equation of one unknown, and concealed problems, which need simultaneous algebraic equations with more than one unknowns

In his book "Kaifukudai no hō" (“Methods for Solving Concealed Problems”) he described important properties related to the tabular notational system

Seki described an old Chinese method for obtaining a root and how he extended the method to get all the real roots of the equation in "Kaiindai no hō" ("Methods for Solving Explict Problems")

"Methods for Solving Implict Problems" was another book in Seki's trilogy

Seki discovered Bernoulli numbers before Jacob Bernoulli. He studied equations containing both positive and negative roots, although he was not aware of complex numbers.

Seki discovered the Newton-Raphson method for solving equations (finds approximations to the zeroes of a real-valued function) and also was responsible for formulating a version of the Newton interpolation polynomial formula

Seki also studied Diophantine equations. In 1683, he considered integer solutions of ax - by = 1 (where a, b are integers)

Seki also developed the elimination theory, which several of his students also helped to develope and improve

In 1685, Seki solved the cubic equation 30 + 14x - 5x^2 - x^3 = 0 utilizing the same method as Horner later would
More of Seki's Achievements


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