Pics of CFs

$\phi$

$\phi=1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\dots}}}}$

phi proper
phi

$\phi=2-\cfrac{1}{2+\cfrac{1}{2-\cfrac{1}{2+\cfrac{1}{2-\dots}}}}$

phi 2 -1 2 1 2 -1 2 1 2 -1 2 etc

$\phi=2-\cfrac{1}{3-\cfrac{1}{3-\cfrac{1}{3-\cfrac{1}{3-\dots}}}}$

2 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 -1 3 phi

$\phi=1+\cfrac{1}{1+\cfrac{2}{2+\cfrac{2}{1+\cfrac{1}{1+\cfrac{1}{1+\dots}}}}}$

1-11-22-21-11-11etc phi

$\phi=1+\cfrac{2}{2+\cfrac{2}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\dots}}}}}$

phi v2

$\phi=1+\cfrac{3}{3+\cfrac{3}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\dots}}}}}$

phi v3

$\pi$

$\pi\approx \cfrac{4}{1+\cfrac{1}{3+\cfrac{4}{5+\cfrac{9}{7}}}}$

pi 0-41-13-45-97 etc

$\pi\approx \cfrac{4}{1+\cfrac{1}{3+\cfrac{4}{5+\cfrac{9}{9}}}}$

pi approx

$e$

$e-1=1+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{4+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{6+\dots}}}}}}}}$

e-1

$\sqrt{2}=1+\cfrac{1}{2+\cfrac{1}{2+\cfrac{1}{2+\cfrac{1}{2+\dots}}}}$

root 2 - 1-12-12-12-12etc

$\sqrt{2}=\cfrac{2}{1+\cfrac{1}{1+\cfrac{2}{1+\cfrac{1}{1+\dots}}}}$

root 2

$\sqrt{3}=1+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{2+\dots}}}}$

root3

$\gamma=\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{4+\cfrac{1}{3+\cfrac{1}{1+\cfrac{1}{13+\dots}}}}}}}}}}$

gamma

$\zeta(3)=1+\cfrac{1}{4+\cfrac{1}{1+\cfrac{1}{18+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{4+\cfrac{1}{9+\cfrac{1}{9+\dots}}}}}}}}}=1.2020569\dots$

zeta 3

$\frac{-2+\sqrt{7}}{3}=1-\cfrac{2}{3-\cfrac{1}{3-\cfrac{2}{3-\cfrac{1}{3-\dots}}}}$

1 -2 3 -1 3 -2 3 -1 3 -2 3 etc - -2pr7 o3

$1=\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\cfrac{2}{1+\dots}}}}$

$1=\cfrac{1}{2-\cfrac{2}{3-\cfrac{2}{3-\cfrac{2}{3-\cfrac{2}{3-\dots}}}}}$

approx 1

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