Liu Hui's π algorithm: Difference between revisions

Revision as of 17:30, 24 August 2024

Revision as of 14:50, 14 March 2025

Line 14:

:"''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, thus with further cut after cut, the area of the resulting polygon will coincide and become one with the circle; there will be no loss''".

This is essentially equivalent to:

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>