# Pi (ATAN three terms) Calculator

## Calculates circular constant Pi using arc tangent (ATAN) series with three terms.

 method Klingensterna 1730 Strassnitzky 1844 Guss 1863 Stormer 1896
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 The calculation ends when two consecutive results are the same.The accuracy of π improves by increasing the number of digits for calculation.Since the discovery of calculus in the 17th century, many mathematicians attempted to calculate Pi using the method of ATAN series expansion. $\normal Gregory\ series\\\hspace{40}tan^{\tiny-1}x=x-{\large\frac{1}{3}}x^3+{\large\frac{1}{5}}x^5-{\large\frac{1}{7}}x^7+\cdot\cdot\cdot\\\vspace{5}(1)\ Klingensterna\ 1730\\\hspace{40}{\large\frac{\pi}{4}}=8tan^{\tiny-1}{\large\frac{1}{10}}-tan^{\tiny-1}{\large\frac{1}{239}}-4tan^{\tiny-1}{\large\frac{1}{515}}\\\vspace{5}(2)\ Strassnitzky\ 1844\\\hspace{40}{\large\frac{\pi}{4}}=tan^{\tiny-1}{\large\frac{1}{2}}+tan^{\tiny-1}{\large\frac{1}{5}}+tan^{\tiny-1}{\large\frac{1}{8}}\\\vspace{5}(3)\ Gauss\ 1863\\\hspace{40}{\large\frac{\pi}{4}}=12tan^{\tiny-1}{\large\frac{1}{18}}+8tan^{\tiny-1}{\large\frac{1}{57}}-5tan^{\tiny-1}{\large\frac{1}{239}}\\\vspace{5}(4)\ Stormer\ 1896\\\hspace{40}{\large\frac{\pi}{4}}=5tan^{\tiny-1}{\large\frac{1}{6}}-tan^{\tiny-1}{\large\frac{1}{43}}-2tan^{\tiny-1}{\large\frac{1}{117}}\\$

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