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- W2048464956 abstract "In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper." @default.
- W2048464956 created "2016-06-24" @default.
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- W2048464956 date "2014-01-01" @default.
- W2048464956 modified "2023-09-26" @default.
- W2048464956 title "On Relations between the General Recurrence Formula of the Extension of Murase-Newton’s Method (the Extension of Tsuchikura*-Horiguchi’s Method) and Horner’s Method" @default.
- W2048464956 doi "https://doi.org/10.4236/am.2014.54074" @default.
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