Taylor series

w用有限来表达无限，由已知到未知，化未知为已知。

https://en.wikipedia.org/wiki/Taylor_series

The Greek philosopher Zeno considered the problem of summing an infinite series to achieve a finite result, but rejected it as an impossibility: the result was Zeno's paradox. Later, Aristotle proposed a philosophical resolution of the paradox, but the mathematical content was apparently unresolved until taken up by Archimedes, as it had been prior to Aristotle by the Presocratic Atomist Democritus. It was through Archimedes's method of exhaustion that an infinite number of progressive subdivisions could be performed to achieve a finite result.^[1] Liu Hui independently employed a similar method a few centuries later.^[2]

In the 14th century, the earliest examples of the use of Taylor series and closely related methods were given by Madhava of Sangamagrama.^[3][4] Though no record of his work survives, writings of later Indian mathematicians suggest that he found a number of special cases of the Taylor series, including those for the trigonometric functions of sine, cosine, tangent, and arctangent. The Kerala school of astronomy and mathematics further expanded his works with various series expansions and rational approximations until the 16th century.

In the 17th century, James Gregory also worked in this area and published several Maclaurin series. It was not until 1715 however that a general method for constructing these series for all functions for which they exist was finally provided by Brook Taylor,^[5] after whom the series are now named.

The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, who published the special case of the Taylor result in the 18th century.

https://zh.wikipedia.org/wiki/刘徽

刘徽（约225年－约295年^[1]），三国时代魏国数学家。白尚恕考证他是山东淄博淄川人，梁敬王刘定国之孙菑乡侯刘逢喜的后裔^[2]。

刘徽为《九章算术》做注，于三国魏景元四年（公元263年）成书，^[3]其中他提出用割圆术计算圆周率的方法，计算出正192边形的面积，得到圆周率的近似值为 {\displaystyle {\tfrac {157}{50}}} (即 3.14)，在此基础上又计算出正3072边形的面积，得到圆周率的近似值为 {\displaystyle {\tfrac {3927}{1250}}} (即 3.1416)。作此书注时，他还依据其“割补术”为证勾股定理，另辟蹊径作青朱出入图。图虽失传，但据其“出入相补、以盈补虚”原理，后人参照书中类似方法还原了此图。

刘徽后撰《重差》，唐初以后失传，仅《重差》一卷单行，因其第一题是测量海岛高度和距离的问题，故又名《海岛算经》。此外刘徽还著有《鲁史欹器图》，《九章重差图》，唐代失传。

刘徽的卓越成就受到后人的重视，宋徽宗时代为恢复数学教学制度，便追封了部分历代的天算家，其中便有刘徽。