# Pi (Viete's formula) Calculator

## Calculates circular constant Pi using the Viete formula.

 $\hspace{20}\frac{2}{\pi}=\sqrt{\frac{1}{2}}\cdot\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}\cdot\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}}\cdot\cdot\cdot\\\vspace{10}$ loop frequency n calculated up to 2n+1-sided polygon 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 The calculation ends when two consecutive results are the same.The accuracy of π improves by increasing the number of digits for calculation.Viete, a French mathematician in the 16th century found the formula of pi the first time.The value of Pi which can be obtained by calculating the nth term is equal to the area of 2n+1-sided regular polygon.Viete's formula　　　　　　　　　　 $\frac{2}{\pi}{\normal=}\sqrt{\frac{1}{2}}\cdot\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}\cdot\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}}\cdot\cdot\cdot\\\vspace{10}\normal(1)\ s_0=0,\hspace{10}y_0=1\\(2)\ s_{n+1}=\sqrt{\large\frac{1+s_n}{2}},\hspace{10}y_{n+1}=y_n s_n\\(3)\ \pi={\large\frac{2}{y_{\infty}}}\\$

Pi (Viete's formula)
 [1-1] /1 Disp-Num5103050100200
[1]  2018/05/14 22:14   Female / Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Find how Viète''s method worked

Sending completion

To improve this 'Pi (Viete's formula) Calculator', please fill in questionnaire.
Male or Female ?
Age

Occupation

Useful?

Purpose of use?