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 />
century, it needed to learn mathematics for business such as simple arithmetics for accounting,<br />
inventory or transportation.<br />
Another application of mathematics was to land survey and map drawing – today’s civil<br />
engineering. Seki was a land surveyor himself. He was intereted strongly in geometry and its<br />
application to land survey. He studied trigonometry and later one of his followers Takebe<br />
Katahiro (1664 - 1739) tried to develop functions sin(x) and arcsin(x) in power series. Takebe<br />
made a table of sinusoidal functions. Takebe also calculated π up to the 41 st decimal place<br />
using an extrapolation method “ruihen zoyaku jutsu” which was proposed in Europe by Lewis<br />
F. Richardson (1881 – 1953) around 1910.<br />
Seki and his followers formulated the bigest school of wasan called Seki ryu. Masters handed<br />
diplomas over disciples. Their mathematical results or contributions were kept rather in secret.<br />
Sometimes Japanese treated wasan as a sort of game or puzzle. Many mathematicians, not<br />
only professionals but also amateurs, competed their skil and wisdom. One anounced<br />
unsolved problem, then the other solved it. Some problems were controversial in which many<br />
people were involved.<br />
Japanese mathematicians published their works writing books. Another way of publication<br />
was sangaku, mathematical tablets which were hung in the Buddhist temples or Shinto shrines<br />
as offerings to the gods or buddhas. The primary meaning of sangaku was to appreciate<br />
mathematicians success, later on it changed to challenges to the congregants.<br />
Seki Takazaku discovered around the year 1680 a method of solving set of simultaneous<br />
equations (elimination theory) which made him closer to computational electromagnetics<br />
where such a procedure is very common. It is a pity that the Eastern and Western<br />
mathematicians had not been in contact as it would have advanced mathematics worldwide<br />
[5].<br />
References<br />
1. Smith David E., Mikami Yoshio, A History of Japanese Mathematics, Dover Pubn. Inc., 2004<br />
(first edition 1914)<br />
2. Ueno Kenji et. al “Seki Takakazu ron josetsu” (Introductory discussions on Seki Takakazu),<br />
Iwanami, Tokyo 2008<br />
3. Gemma Koichi „Wasan ka monogatari – Seki Takakazu to Koshu no monka tachi” (Japanese<br />
mathematicians – Seki Takakazu and his followers in Koshu), Sogensha, Tokyo 2008<br />
4. Tohoku University Wasan Portal (http://www2.library.tohoku.ac.jp/wasan/)<br />
5. Normile Dennis, Samurai Mathematician Set Japan Ablaze with Brief, Bright Light, Science,<br />
10 October 2008, vol. 322<br />
164
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