# Pi (ATAN two terms) Calculator

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

 method J. Machin 1706 J. Hermann 1706 L. Euler 1738 L. Euler/G. Vega 1755 C. Hutton 1776 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.$\normal Gregory\ series\\\hspace{40}tan^{\tiny-1}x=x-{\large\frac{1}{3}}x^3+{\large\frac{1}{5}}x^5-{\large\frac{1}{7}}x^7+\cdot\cdot\cdot\\(1)\ Leibniz\ 1671\\\vspace{5}\hspace{40}{\large\frac{\pi}{4}}=tan^{\tiny-1}\ 1=1-{\large\frac{1}{3}}+{\large\frac{1}{5}}-{\large\frac{1}{7}}+\cdot\cdot\cdot\\\vspace{5}(2)\ Machin\ 1706\\\hspace{40}{\large\frac{\pi}{4}}=4tan^{\tiny-1}{\large\frac{1}{5}}-tan^{\tiny-1}{\large\frac{1}{239}}\\\vspace{5}(3)\ Hermann\ 1706\\\hspace{40}{\large\frac{\pi}{4}}=2tan^{\tiny-1}{\large\frac{1}{3}}+tan^{\tiny-1}{\large\frac{1}{7}}\\\vspace{5}(4)\ Euler\ 1738\\\hspace{40}{\large\frac{\pi}{4}}=tan^{\tiny-1}{\large\frac{1}{2}}+tan^{\tiny-1}{\large\frac{1}{3}}\\\vspace{5}(5)\ Euler\ &\ Vega\ 1755\\\hspace{40}{\large\frac{\pi}{4}}=5tan^{\tiny-1}{\large\frac{1}{7}}+2tan^{\tiny-1}{\large\frac{3}{79}}\\\vspace{5}(6)\ Hutton\ 1776\\\hspace{40}{\large\frac{\pi}{4}}=2tan^{\tiny-1}{\large\frac{1}{3}}+tan^{\tiny-1}{\large\frac{1}{7}}\\$

Pi (ATAN two terms)
 [0-0] / 0 Disp-Num5103050100200
The message is not registered.

Sending completion

To improve this 'Pi (ATAN two terms) Calculator', please fill in questionnaire.
Male or Female ?
Age

Occupation

Useful?

Purpose of use?