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Arima Yoriyuki (有馬 頼徸, December 31, 1714 – December 16, 1783) was a Japanese mathematician of the Edo period. He was the lord of Kurume Domain.

He approximated the value of ${\displaystyle \pi }$ and its square, ${\displaystyle \pi ^{2}}$. In 1766, he found the following rational approximation of ${\displaystyle \pi }$, correct to 29 digits:

${\displaystyle \pi \approx {\frac {428224593349304}{136308121570117}}=3.14159265358979323846264338327(569...).}$

References

1. "Collection of approximations for ${\displaystyle \pi }$". Retrieved April 4, 2008.
2. Hardy, G. H.; E. M. Wright (1978). An Introduction to the Theory of Numbers. Oxford Science Publications.

Further reading

• Döll, Steffen; Hinz, Andreas M. (2018). "Kyū-renkan – the Arima sequence". In Ogawa, T.; Morimoto, M. (eds.). Mathematics of Takebe Katahiro and History of Mathematics in East Asia. Advanced Studies in Pure Mathematics. Vol. 79. Tokyo: Mathematical Society of Japan. pp. 321–335.

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