The idea of limits arises from seeking accurate solutions to certain practical problems. For example, the mathematician Liu Hui used the method of inscribing a regular polygon in a circle to calculate the area of a circle - the method of cutting a circle, which is the application of limit thinking in geometry. The figure below gives an example of approximating the area of a circle with a regular 12-sided polygon (area ) inscribed in the unit circle.

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        For another example, the philosopher Zhuangzi ( century BC) during the Spring and Autumn Period and the Warring States Period had a famous saying in "Zhuangzi·Tianxia Chapter" on the issue of " cutting off a foot " : " If you take a stick of one foot, half of it will be taken every day, and it will be inexhaustible for eternity . " It also contains profound extreme thoughts.

[ Animation Demonstration ]