Abstract
In the 17th century, Japanese mathematicians could calculate the arc length numerically at any accuracy once the diameter and the sagitta were given numerically. But they could not find any formulas to express the arc length in terms of the diameter and the sagitta; only polynomials or fractions of polynomials were considered as formulas. Finally in 1722, Takebe Katahiro (1664–1739) succeeded in expressing the arc length in terms of the diameter and the sagitta in the form of an infinite series expression.
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© 2013 Springer Japan
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Morimoto, M. (2013). Takebe Katahiro’s Algorithms for Finding the Circular Arc Length. In: Knobloch, E., Komatsu, H., Liu, D. (eds) Seki, Founder of Modern Mathematics in Japan. Springer Proceedings in Mathematics & Statistics, vol 39. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54273-5_22
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DOI: https://doi.org/10.1007/978-4-431-54273-5_22
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