Liu Hui's π algorithm: Difference between revisions

Revision as of 02:21, 13 November 2018

Revision as of 02:22, 13 November 2018

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: <math>{} m = \sqrt{\left(\tfrac{M}{2}\right)^2 + \left(r - \sqrt{r^2- \tfrac{M^2}{4}}\right)^2}</math>

From here, there is now a technique to determine {{math|m}} from {{math|M}}, which gives the side length for a polygon with twice the number of edges. Starting with a [[hexagon]], Liu Hui could determine the side length of a dodecagon using this formula. Then continue repetitively to determine the side length of aan 24-gon[[icositetragon]] given the side length of a dodecagon. He could do this recursively as many times as necessary. Knowing how to determine the area of these polygons, Liu Hui could then approximate {{pi}}.

With <math>r = 10</math> units, he obtained