XIX Sympozjum Srodowiskowe PTZE - materialy.pdf
XIX Sympozjum Srodowiskowe PTZE - materialy.pdf
XIX Sympozjum Srodowiskowe PTZE - materialy.pdf
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<strong>XIX</strong> <strong>Sympozjum</strong> <strong>PTZE</strong>, Worliny 2009<br />
JAPANESE MATHEMATICS<br />
AND ENGINEERINGS DURING THE EDO PERIOD<br />
Mitsuhiko Toho 1 , Andrzej Krawczyk 2<br />
1 Polish Japanese Institute of Information Technology, Warsaw, Poland<br />
2 Czestochowa University of Technology, Częstochowa, Poland<br />
Mathematics developed in Japan during the Edo period (1603 – 1868) is called wasan. Japan<br />
was closed and isolated from the rest of the world in that period. Therefore the style of wasan<br />
is very different from European. However, some ideas of Japanese mathematicians are very<br />
close to which developed in Europe. Wasan owed its big part to Chinese mathematics but<br />
mathematicians of each countries developed in different way.<br />
Good examples can be found in works of the most eminent Japanese mathematician Seki<br />
Takakazu (1642?-1708) (Fig.1).<br />
In 1674 Seki published “Hatsubi sanpo” in which he solved 15<br />
problems given by Sawaguchi Kazuyuki in his book “Kokon<br />
sanpo ki” in 1671. Seki solved, for example, high order<br />
algebraic equations with several variables using a method<br />
known today as the Newtonean method, an application of<br />
differential calculus. Seki also calculated surfaces and volumes<br />
of geometrical figures such as circles, elipses, spheres<br />
developing ideas of integration. The method of differentiation<br />
and integration was established by Newton and Leibniz almost<br />
the same time in Europe. Seki’s accuracy of π reached to the<br />
11 th decimal place which was the world record at that time.<br />
Fig. 1. Seki Takazaku<br />
Seki and other Japanese mathematicians solved problems numerically. They used counting<br />
rods sangi and abacus soroban to operations of algebraic formulae and numerical calculations<br />
respectively. Soroban was imported from China not later than the middle of the16 th century. It<br />
became more and more popular in Japan up to today.<br />
Before the Edo period in Japan traditional mathematicians concerned with astronomy and<br />
astrology to make calendars which fit agriculture. All mathematical ideas and tools were<br />
introduced from China. When the monetary economy was developed at the end of 16 th<br />
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