Π day

[Thomas Klemm]

(03-14-2022 03:35 AM)robve Wrote:  What's your favorite pi series?

Not a series but I like Vieta's Formula for Pi since only 2 is used:

\(
\begin{align}
\pi = 2
\times \frac{2}{\sqrt{2}}
\times \frac{2}{\sqrt{2 + \sqrt{2}}}
\times \frac{2}{\sqrt{2 + \sqrt{2 + \sqrt{2}}}}
\times \frac{2}{\sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2}}}}}
\times \cdots
\end{align}
\)

Code:

00 { 30-Byte Prgm }
01▸LBL "VIETA"
02 2
03 ENTER
04 ENTER
05 STO 00
06 0
07▸LBL 00
08 RCL+ ST T
09 SQRT
10 ÷
11 STO× 00
12 X<> ST L
13 VIEW 00
14 GTO 00
15 END

R00=2.82842712475
x: 1.41421356237

R00=3.06146745892
x: 1.84775906502

R00=3.12144515226
x: 1.96157056081

R00=3.13654849055
x: 1.99036945334

R00=3.14033115695
x: 1.99759091241

R00=3.14127725093
x: 1.99939763739

R00=3.14151380114
x: 1.99984940368

R00=3.14157294037
x: 1.99996235057

R00=3.14158772528
x: 1.99999058762

R00=3.14159142151
x: 1.99999764690

R00=3.14159234557
x: 1.99999941173

R00=3.14159257658
x: 1.99999985293

R00=3.14159263434
x: 1.99999996323

R00=3.14159264878
x: 1.99999999081

R00=3.14159265239
x: 1.99999999770

R00=3.14159265329
x: 1.99999999943

R00=3.14159265351
x: 1.99999999986

R00=3.14159265357
x: 1.99999999996

R00=3.14159265359
x: 1.99999999999

R00=3.14159265359
x: 2.00000000000