圓周率計算（ATAN 3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。

\(\normalsize Gregory\ series\\ \hspace{40px}tan^{\tiny-1}x=x-{\large\frac{1}{3}}x^3+{\large\frac{1}{5}}x^5-{\large\frac{1}{7}}x^7+\cdot\cdot\cdot\\ (1)\ Klingensterna\ 1730\\ \hspace{40px}{\large\frac{\pi}{4}}=8tan^{\tiny-1}{\large\frac{1}{10}}-tan^{\tiny-1}{\large\frac{1}{239}}-4tan^{\tiny-1}{\large\frac{1}{515}}\\ (2)\ Strassnitzky\ 1844\\ \hspace{40px}{\large\frac{\pi}{4}}=tan^{\tiny-1}{\large\frac{1}{2}}+tan^{\tiny-1}{\large\frac{1}{5}}+tan^{\tiny-1}{\large\frac{1}{8}}\\ (3)\ Gauss\ 1863\\ \hspace{40px}{\large\frac{\pi}{4}}=12tan^{\tiny-1}{\large\frac{1}{18}}+8tan^{\tiny-1}{\large\frac{1}{57}}-5tan^{\tiny-1}{\large\frac{1}{239}}\\ (4)\ Stormer\ 1896\\ \hspace{40px}{\large\frac{\pi}{4}}=5tan^{\tiny-1}{\large\frac{1}{6}}-tan^{\tiny-1}{\large\frac{1}{43}}-2tan^{\tiny-1}{\large\frac{1}{117}}\\\)