计算圆周率的马青公式

mathematica

lsr314 发表于 2020-11-27 00:11
我知道你是怎么得来的了，利用了$37=6^2+1$

不知道你说的是什么意思！

mathematica

lsr314 发表于 2020-11-27 10:47
你不是要三项吗，那里三项，四项的都有，引用的已经是目前最好的结果了

1. 3 ArcTan[4291039/99429196] + 13 ArcTan[5/99] // FullSimplify

复制代码

\[13 \tan ^{-1}\left(\frac{5}{99}\right)+3 \tan ^{-1}\left(\frac{4291039}{99429196}\right)\]

mathematica

1. 22 ArcTan[17014395978641495719/2082431079356889478358] +
   
2.   61 ArcTan[685601/69049993] // FullSimplify

复制代码

\[61 \tan ^{-1}\left(\frac{685601}{69049993}\right)+22 \tan ^{-1}\left(\frac{17014395978641495719}{2082431079356889478358}\right)\]

数值差不多是
\[22 \tan ^{-1}(0.00817)+61 \tan ^{-1}(0.009929)\]

mathematica

1. -5 ArcTan[685601/69049993] + 22 ArcTan[3/79] // FullSimplify

复制代码

\[22 \tan ^{-1}\left(\frac{3}{79}\right)-5 \tan ^{-1}\left(\frac{685601}{69049993}\right)\]

lsr314

1. 99 ArcTan[
   
2.    1066267149847167315579490402377505014663714733521178290558922528826156648535722953801728/
   
3.     222470405377470850243091288520397821267361269882560150856229364406815305926180285924245504] +
   
4. 61 ArcTan[
   
5.    73123064661737095669076253640742568023997954450880942347488866948225235649393566591906074883237721849797739019331681382942445067399730735087616/143465071652824076575215971184919343183382031844826666248161147\
   
6. 01130022719688619467831547383263177604653341129782632370199793422082470802318426112]

复制代码

$99 ArcTan[1066267149847167315579490402377505014663714733521178290558922528826156648535722953801728/222470405377470850243091288520397821267361269882560150856229364406815305926180285924245504]+ 61 ArcTan[73123064661737095669076253640742568023997954450880942347488866948225235649393566591906074883237721849797739019331681382942445067399730735087616/14346507165282407657521597118491934318338203184482666624816114701130022719688619467831547383263177604653341129782632370199793422082470802318426112]$
比值分别是0.00479285和0.00509692

mathematica

lsr314 发表于 2020-11-27 14:26
$99 ArcTan[1066267149847167315579490402377505014663714733521178290558922528826156648535722953801728/ ...

你可以说说你的是怎么搞出来的