# 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
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 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　　　　　　　　　　 $\frac{2}{\pi}{\normal=}\sqrt{\frac{1}{2}}\cdot\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}\cdot\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}}\cdot\cdot\cdot\\\vspace{10}\normal(1)\ s_0=0,\hspace{10}y_0=1\\(2)\ s_{n+1}=\sqrt{\large\frac{1+s_n}{2}},\hspace{10}y_{n+1}=y_n s_n\\(3)\ \pi={\large\frac{2}{y_{\infty}}}\\$

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