圓周率計算（ATAN 4 項級數）

當上一次與本次的計算結果相等時，程式即結束。增加運算位數可提升π的計算精度。

隨著微積分學在17世紀的發展，許多數學家嘗試運用atan(x)的級數展開法來計算圓周率。

\(\normalsize Gregory\ series\hspace{10px}tan^{\tiny-1}x=x-{\normalsize\frac{1}{3}}x^3+{\normalsize\frac{1}{5}}x^5-{\normalsize\frac{1}{7}}x^7+\cdot\cdot\cdot\\ (1)\ Gauss\ 1863\\ \hspace{10px}{\small{\normalsize\frac{\pi}{4}}=12tan^{\tiny-1}{\normalsize\frac{1}{38}}+20tan^{\tiny-1}{\normalsize\frac{1}{57}}+7tan^{\tiny-1}{\normalsize\frac{1}{239}}+24tan^{\tiny-1}{\normalsize\frac{1}{268}}}\\ (2)\ Stormer\ 1896\\ \hspace{10px}{\small{\normalsize\frac{\pi}{4}}=44tan^{\tiny-1}{\normalsize\frac{1}{57}}+7tan^{\tiny-1}{\normalsize\frac{1}{239}}-12tan^{\tiny-1}{\normalsize\frac{1}{682}}+24tan^{\tiny-1}{\normalsize\frac{1}{12943}}}\\ (3)\ Escott\ 1896\\ \hspace{10px}{\small{\normalsize\frac{\pi}{4}}=22tan^{\tiny-1}{\normalsize\frac{1}{28}}+2tan^{\tiny-1}{\normalsize\frac{1}{443}}-5tan^{\tiny-1}{\normalsize\frac{1}{1393}}-10tan^{\tiny-1}{\normalsize\frac{1}{11018}}}\\ (4)\ K.\ Takano\ 1982\\ \hspace{10px} {\small{\normalsize\frac{\pi}{4}}=12tan^{\tiny-1}{\normalsize\frac{1}{49}}+32tan^{\tiny-1}{\normalsize\frac{1}{57}}-5tan^{\tiny-1}{\normalsize\frac{1}{239}}+12tan^{\tiny-1}{\normalsize\frac{1}{110443}}}\\ (5)\ T.\ Murata\ 1982\\ \hspace{10px}{\small{\normalsize\frac{\pi}{4}}=24tan^{\tiny-1}{\normalsize\frac{1}{36}}+8tan^{\tiny-1}{\normalsize\frac{1}{57}}-5tan^{\tiny-1}{\normalsize\frac{1}{239}}-12tan^{\tiny-1}{\normalsize\frac{1}{23382}}}\\ (6)\ A.\ Shibata\ 1983\\ \hspace{10px}{\small{\normalsize\frac{\pi}{4}}=24tan^{\tiny-1}{\normalsize\frac{1}{43}}+20tan^{\tiny-1}{\normalsize\frac{1}{57}}-12tan^{\tiny-1}{\normalsize\frac{1}{117}}-5tan^{\tiny-1}{\normalsize\frac{1}{239}}}\\\)