Amar Pi

3,14159 26535 89793 23846 26433...

Amar Pi ($\pi$), namey amarê daireyo ke matematik de esto.

Amaro Pi

Be nameyê Rıstımê Arşimedi ya zi Amarê Ludolphi ra zi şınasiyeno. Terim amar pi Yunanki πίτα (píta) ra yeno, be kılmkerdış beno herfa Yunanki π "pi". Amar Pi, yew Amaro İrrasyonelo. Matematik u fizik de zaf formulan de yeno gırweynaene (xebetnaene). Amaro Pi, nezdiyê :$\pi \approx 3{,}141592654$ ya zi nezdiyê ${\tfrac {22}{7}}$o.

Taê formulê Pi ($\pi$)

Nilakantha Somayaji:

$\pi ={3}+{\frac {4}{{3^{3}}-3}}-{\frac {4}{{5^{3}}-5}}+{\frac {4}{{7^{3}}-7}}-{\frac {4}{{9^{3}}-9}}+...$

$\pi ={3}+{\frac {4}{2\times 3\times 4}}-{\frac {4}{4\times 5\times 6}}+{\frac {4}{6\times 7\times 8}}-{\frac {4}{8\times 9\times 10}}+...$

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Franciscus Vieta:

$\pi =2\times {\frac {2}{\sqrt {2}}}\times {\frac {2}{\sqrt {2+{\sqrt {2}}}}}\times {\frac {2}{\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}}\times {\frac {2}{\sqrt {2+{\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}}}}\times \cdots$

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Gregory–Leibniz:

$\pi =4\sum _{n=0}^{\infty }{\cfrac {(-1)^{n}}{2n+1}}=4\left({\frac {1}{1}}-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+-\cdots \right)\!={\cfrac {4}{1+{\cfrac {1^{2}}{2+{\cfrac {3^{2}}{2+{\cfrac {5^{2}}{2+\ddots }}}}}}}}\!$

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Isaac Newton:

$\pi =\sum _{n=0}^{\infty }{\cfrac {{2^{n+1}}\cdot {(n!)^{2}}}{(2n+1)!}}$

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Leonhard Euler:

$\pi =-i\ln(-1)$

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Bailey-Borwein-Plouffe:

$\pi =\sum _{n=0}^{\infty }{\biggl (}{\frac {1}{16}}{\biggr )}^{n}\left({\frac {4}{8n+1}}-{\frac {2}{8n+4}}-{\frac {1}{8n+5}}-{\frac {1}{8n+6}}\right)$

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