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Double sharp (talk | contribs) →Area of a circle: restore some text that appears to have been cut off (vandalistically?) halfway |
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Liu Hui argued:
:"''Multiply one side of a hexagon by the radius (of its circumcircle), then multiply this by three, to yield the area of a dodecagon; if we cut a hexagon into a dodecagon, multiply its side by its radius, then again multiply by six, we get the area of a 24-gon; the finer we cut, the smaller the loss with respect to the area of circle,
Apparently Liu Hui had already mastered the concept of the limit<ref>First noted by Japanese mathematician [[Yoshio Mikami]]</ref>
: <math>\lim_{N \to \infty}\text{area of }N\text{-gon} = \text{area of circle}. \, </math>
Further, Liu Hui proved that the area of a circle is half of its circumference multiplied by its radius. He said:
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