Pi greco – ValCon.It

Pi greco compare in geometria…

$C = 2\pi r$

$A = \pi a b$

$A = \pi r^2$

$S = 2\pi r (r+h)$

$S = 4 \pi r^2$

$V = \pi r^2 h$

$\displaystyle V = \frac{4}{3} \pi r^3$

Pi greco compare in molte… formule notevoli

$e^{i \pi}+1=0$

$\displaystyle n!\approx \sqrt{2 \pi n} \left( \frac{n}{e} \right)^{n}$

$\displaystyle T=2\pi \sqrt{\frac{l}{g}}$

$\displaystyle f(x)=\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2 {\sigma}^2}}$

$\displaystyle\int_{0}^{+\infty}\,e^{-x^2}\,dx=\sqrt{\frac{\pi}{4}}$

$\displaystyle\int_{-\infty}^{+\infty}\,e^{-x^2}\,dx=\sqrt{\pi}$

$\displaystyle \int_{-\infty}^{+\infty}\,e^{-\frac{x^2}{2}}\,dx=\sqrt{2\pi}$

$\displaystyle\int_{-\infty}^{+\infty}\,\frac{\sin{x}}{x}\,dx=\pi$

$\displaystyle\int_{-\infty}^{+\infty}\cos{(x^2)}\,dx=\sqrt{\frac{\pi}{2}$

$\displaystyle\int_{-\infty}^{+\infty}\sin{(x^2)}\,dx=\sqrt{\frac{\pi}{2}$

$\displaystyle\int_{-\infty}^{+\infty}\,\frac{1}{1+x^2}\,dx=\pi$

$\displaystyle\int_{0}^{1}\,\frac{1}{1+x^2}\,dx=\frac{\pi}{4}$

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