Births on December 31

Arima Yoriyuki, Japanese mathematician and educator (d. 1783)

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







π





{\displaystyle \pi }

and its square,









π



2









{\displaystyle \pi ^{2}}

. In 1766, he found the following rational approximation of







π





{\displaystyle \pi }

, correct to 29 digits:







π

≈





428224593349304

136308121570117





=

3.14159265358979323846264338327

(

569...

)

.





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