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Takebe Katahiro (建部 賢弘, 1664 – August 24, 1739), also known as Takebe Kenkō, was a Japanese mathematician and cartographer during the Edo period.

Biography

Takebe was the favorite student of the Japanese mathematician Seki Takakazu Takebe is considered to have extended and disseminated Seki's work.

In 1706, Takebe was offered a position in the Tokugawa shogunate's department of ceremonies.

In 1719, Takebe's new map of Japan was completed; and the work was highly valued for its quality and detail.

Shōgun Yoshimune honored Takebe with rank and successively better positions in the shogunate.

Legacy

Takebe played a critical role in the development of the Enri (円理, "circle principle") - a crude analogon to the western calculus. He also created charts for trigonometric functions.

He achieved a power series expansion of ${\displaystyle (\arcsin(x))^{2}}$ in 1722, 15 years earlier than Euler. This was the first power series expansion obtained in Wasan. This result was first conjectured by heavy numeric computation.

He used the Richardson extrapolation in 1695, about 200 years earlier than Richardson.

He also computated 41 digits of ${\displaystyle \pi }$, based on polygon approximation and the Richardson extrapolation.

Takebe Prizes

In the context of its 50th anniversary celebrations, the Mathematical Society of Japan established the Takebe Prize and the Takebe Prizes for the encouragement of young people who show promise as mathematicians.

Selected works

In a statistical overview derived from writings by and about Takebe Kenko, OCLC/WorldCat encompasses roughly 10+ works in 10+ publications in 3 languages and 10+ library holdings.

• 1683 – Kenki sanpō (研幾算法) OCLC 22056510086
• 1685 – Hatsubi sanpō endan genkai (發微算法演段諺解) OCLC 22056085721

See also

• Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in shinto shrines
• Soroban, a Japanese abacus
• Japanese mathematics
• Richardson extrapolation

Notes

1. ^ Smith, David. (1914). A History of Japanese Mathematics, p. 146. , p. 146, at Google Books
2. "Takebe Katahiro", Encyclopædia Britannica online.
3. Jochi, Shigeru. (1997). "Takebe Katahiro," Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, p. 932. , p. 932, at Google Books
4. ^ Mathematical Society of Japan, Takebe Prize
5. Osada, Naoki (Aug 26, 2011). "収束の加速法の歴史 : 17世紀ヨーロッパと日本の加速法 (数学史の研究)" (PDF). Study of the History of Mathematics RIMS Kôkyûroku (in Japanese). 1787: 100–102 – via Kyoto University.
6. Ogawa, Tsugane (May 13, 1997). "円理の萌芽 : 建部賢弘の円周率計算 : (数学史の研究)" (PDF). Study of the History of Mathematics RIMS Kôkyûroku (in Japanese). 1019: 80–88 – via Kyoto University.
7. WorldCat Identities: 建部賢弘 1664-1739

References

• Endō Toshisada (1896). History of mathematics in Japan (大日本數學史, Dai Nihon sūgakushi). Tōkyō: _____. OCLC 122770600
• Horiuchi, Annick. (1994). Les Mathematiques Japonaises a L'Epoque d'Edo (1600–1868): Une Etude des Travaux de Seki Takakazu (?-1708) et de Takebe Katahiro (1664–1739). Paris: Librairie Philosophique J. Vrin. ISBN 9782711612130; OCLC 318334322
• Selin, Helaine, ed. (1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Dordrecht: Kluwer/Springer. ISBN 9780792340669; OCLC 186451909
• David Eugene Smith and Yoshio Mikami. (1914). A History of Japanese Mathematics. Chicago: Open Court Publishing. OCLC 1515528 -- note alternate online, full-text copy at archive.org
• O'Connor, John J.; Robertson, Edmund F., "Takebe Katahiro", MacTutor History of Mathematics Archive, University of St Andrews

• 1664 births
• 1739 deaths
• 17th-century Japanese mathematicians
• 18th-century cartographers
• 18th-century Japanese mathematicians
• Japanese writers of the Edo period