Talk:Liu Xin (scholar)

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Pi

A taiwanese source transmits us the following interpretation of the text: there are apparently 10 inches to a chinese foot, so diameter is sqrt(50)+0.095, where 0.095 inches is the gap between the corner of the square and the circle. Assuming the area is 162 inches, the pi comes out to be 3.1547 --- close but not nearly as good as Archimedes three hundred years earlier with his 22/7 < pi< 223/71. See here: http://episte.math.ntu.edu.tw/articles/mm/mm_03_2_08/page2.html Kotika98 (talk) 03:22, 5 May 2014 (UTC)[reply]

This seems to imply the formula

\pi ={\frac {A}{r^{2}}}={\frac {162}{({\sqrt {5}}0+0.095)^{2}}}

, though diameter and radius appear to be confused and the area should be in square inches. Checking with a calculator I see 162÷(√50+0.095)² ≈ 3.154664564 PJTraill (talk) 15:32, 6 August 2018 (UTC)[reply]

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Did he calculate π or just measure?

Could it be that Liu Xin used no mathematical theory but gave figures based on measurement? If this doubt can be scattered, it would be good to mention it, along with the reasoning, in the section #pi. PJTraill (talk) 13:04, 6 August 2018 (UTC)[reply]