Abstract
The method of successive divisions developed by Wasan mathematicians was considered as a kind of Diophantine approximations. Nevertheless their main aim is not to find the close approximating fractions of irrational numbers but to obtain the simple fractions which enter the assigned range. We shall here reproduce their crucial algorithm. About fifty years later another Wasan mathematician made an alternate treatment for the same problem which is rather troublesome but gives systematical and complete solutions.
This note was published in Japanese with some additional remarks.”Ruiyaku-jutsu, An algorithm for the solution to the indefinite inequality of Diophantine type”, The Bulletin of Wasan Institute, No.8, 2008, pp.3–14.
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© 2013 Springer Japan
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Tsuchikura, T. (2013). The Method of Successive Divisions by Takebe Katahiro and Nakane Genkei. 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_23
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DOI: https://doi.org/10.1007/978-4-431-54273-5_23
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