数学圆周率计算马青公式π/4=4arctan1/5-arctan1/239如何得出的?
问题补充说明:马青当年是如何计算出π/4=4arctan1/5-arctan1/239,而且会和π的准确数值如此接近,到了500多位,只是知道,但是完全不了解他怎么得出这个式子的
设
x县玉民误市主点=arctanA
tanx=A
困tan2x=(2tanx)/(1-tan^2x)
tan2x=(2A)/来自(1-A^2)
2x=arctan((2A)/(1-A^2))
2arctanA=arctan((2A)/(1-A^2))
4arct千般界度低而anA=2arctan((2A)/(1-A^2))
A=1/5
4arctan(1/5)=2arctan((2/5)/(1-1/25))=2arctan(5/12)
2arctan(5/12)-arctan(1/239)
=arctan((2*5/12)/(1-25/144))-arctan(1/239)
=arctan(120/119)-arcta包如儿角样屋婷协n(1/239)
=arctan((120/119-1/239)/(1+120/119*1/239)
=arctan(1.0042/1.0042)
=arctan(1)
=π/4
标签:马青,4arctan1,arctan1