숫자 2와 파이, 작은 전시회

\cos\frac{\pi}{4}=\cos\frac{\pi}{2^2}= \frac{\sqrt{2}}{2}

\cos \frac{\pi}{8}=\cos\frac{\pi}{2^3}= \frac{\sqrt{2+\sqrt{2}}}{2}

\cos \frac{\pi}{16}=\cos\frac{\pi}{2^4}= \frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2}

\cos \frac{\pi}{32}=\cos\frac{\pi}{2^5}=  \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}{2}

\cos \frac{\pi}{64}=\cos\frac{\pi}{2^6}= \frac{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}}{2}

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

http://en.wikipedia.org/wiki/Viète's_formula

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