# Pi (ATAN four terms) Calculator

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

 rm method C.F. Gauss 1863 F.C.M. Stormer 1896 E.B. Escott 1896 K. Takano 1982 T. Murata 1982 A. Sibata 1983 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 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.$\normal Gregory\ series\hspace{10}tan^{\tiny-1}x=x-{\normal\frac{1}{3}}x^3+{\normal\frac{1}{5}}x^5-{\normal\frac{1}{7}}x^7+\cdot\cdot\cdot\\\vspace{5}(1)\ Gauss\ 1863\\\hspace{10}{\small{\normal\frac{\pi}{4}}=12tan^{\tiny-1}{\normal\frac{1}{38}}+20tan^{\tiny-1}{\normal\frac{1}{57}}+7tan^{\tiny-1}{\normal\frac{1}{239}}+24tan^{\tiny-1}{\normal\frac{1}{268}}}\\\vspace{5}(2)\ Stormer\ 1896\\\hspace{10}{\small{\normal\frac{\pi}{4}}=44tan^{\tiny-1}{\normal\frac{1}{57}}+7tan^{\tiny-1}{\normal\frac{1}{239}}-12tan^{\tiny-1}{\normal\frac{1}{682}}+24tan^{\tiny-1}{\normal\frac{1}{12943}}}\\\vspace{5}(3)\ Escott\ 1896\\\hspace{10}{\small{\normal\frac{\pi}{4}}=22tan^{\tiny-1}{\normal\frac{1}{28}}+2tan^{\tiny-1}{\normal\frac{1}{443}}-5tan^{\tiny-1}{\normal\frac{1}{1393}}-10tan^{\tiny-1}{\normal\frac{1}{11018}}}\\\vspace{5}(4)\ K.\ Takano\ 1982\\\hspace{10} {\small{\normal\frac{\pi}{4}}=12tan^{\tiny-1}{\normal\frac{1}{49}}+32tan^{\tiny-1}{\normal\frac{1}{57}}-5tan^{\tiny-1}{\normal\frac{1}{239}}+12tan^{\tiny-1}{\normal\frac{1}{110443}}}\\\vspace{5}(5)\ T.\ Murata\ 1982\\\hspace{10}{\small{\normal\frac{\pi}{4}}=24tan^{\tiny-1}{\normal\frac{1}{36}}+8tan^{\tiny-1}{\normal\frac{1}{57}}-5tan^{\tiny-1}{\normal\frac{1}{239}}-12tan^{\tiny-1}{\normal\frac{1}{23382}}}\\\vspace{5}(6)\ A.\ Shibata\ 1983\\\hspace{10}{\small{\normal\frac{\pi}{4}}=24tan^{\tiny-1}{\normal\frac{1}{43}}+20tan^{\tiny-1}{\normal\frac{1}{57}}-12tan^{\tiny-1}{\normal\frac{1}{117}}-5tan^{\tiny-1}{\normal\frac{1}{239}}}\\$

Pi (ATAN four terms)
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