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Takebe Katahiro’s Algorithms for Finding the Circular Arc Length

  • Mitsuo Morimoto
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 39)

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.

Keywords

Maximum Error Approximation Formula Rational Formula Half Circle Slight Sign 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.TokyoJapan

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