Pi Calculation (Viète’s Formula)
Calculate pi (π) using Viète’s formula.
The calculation ends when the current value matches the previous one. Increasing the number of digits used in the calculation improves the precision of π.
The 16th-century French mathematician Viète was the first to derive a formula for calculating pi.
The value of π obtained up to the nth term is equal to the area of a 2^(n+1)-sided polygon.
Viète’s Formula for Pi
The 16th-century French mathematician Viète was the first to derive a formula for calculating pi.
The value of π obtained up to the nth term is equal to the area of a 2^(n+1)-sided polygon.
Viète’s Formula for Pi
| \(\frac{2}{\pi}{\normalsize=}\sqrt{\frac{1}{2}}\cdot\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}\cdot\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}}\cdot\cdot\cdot\\normalsize (1)\ s_0=0,\hspace{10px}y_0=1\\ (2)\ s_{n+1}=\sqrt{\large\frac{1+s_n}{2}},\hspace{10px}y_{n+1}=y_n s_n\\ (3)\ \pi={\large\frac{2}{y_{\infty}}}\\ \) |
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