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

Sending completion

To improve this 'Pi (ATAN two terms) Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?