Takebe was the favorite student of 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.
Takebe played 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 obtained power series expansion of 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 Richardson extrapolation, about 200 years earlier than Richardson.
He also computated 41 digits of , based on polygon approximation and Richardson extrapolation.
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.
- 1683 — Kenki sanpō (研幾算法) OCLC 22056510086
- 1685 — Hatsubi sanpō endan genkai (發微算法演段諺解) OCLC 22056085721
- Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in shinto shrines
- Soroban, a Japanese abacus
- Japanese mathematics (wasan)
- Richardson extrapolation
- Smith, David. (1914). A History of Japanese Mathematics, p. 146. , p. 146, at Google Books
- "Takebe Katahiro," Encyclopædia Britannica online.
- 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
- Mathematical Society of Japan, Takebe Prize
- WorldCat Identities: 建部賢弘 1664-1739
- 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.