Liu Hui's π algorithm: Difference between revisions

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Corrected typo in Iterative Algorithm. Said "AOP, APC are two..." should be "APO, APC are two..."
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Bisect {{math|AB}} with line {{math|OPC}}, {{math|AC}} becomes one side of [[dodecagon]] (12-gon), let its length be {{math|m}}. Let the length of {{math|PC}} be {{math|j}} and the length of {{math|OP}} be {{math|G}}.
 
{{math|AOPAPO}}, {{math|APC}} are two right angle triangles. Liu Hui used the [[Pythagorean theorem]] repetitively:
 
: <math>{} G^2 = r^2 - \left(\tfrac{M}{2}\right)^2</math>