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Takebe Katahiro

Japanese Mathematician and Disciple of Seki Takakazu

Takebe Katahiro (1664–1739) was a brilliant Japanese mathematician of the Edo period and a direct disciple of Seki Takakazu. He expanded upon his teacher’s legacy, particularly in the study of series, interpolation, and approximation methods.

Takebe is credited with introducing techniques equivalent to Taylor expansions. He developed polynomial interpolation formulas that closely resembled Newton’s forward-difference method. For example, he worked with expansions of sine functions: \[ \sin x \approx x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots \] Though not expressed in modern notation, his results demonstrated deep insight into infinite processes.

He applied these methods to astronomy, calculating solar and lunar motions with high precision. His achievements also included contributions to mapmaking and navigation, essential for Japan’s maritime activities.

Takebe’s work reflected the high sophistication of wazan and showed that Japanese mathematics had reached concepts strikingly similar to early European calculus. As a loyal student of Seki, he preserved and transmitted this intellectual tradition, ensuring its survival for future generations of Japanese scholars.