Gallery of continued fractions

regular/repeating

    \[\text{golden ratio } \phi =\frac{\sqrt{5}-1}{2} = \cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\dots}}}}=0.618033988749895\dots\]

    \[ \sqrt{2} =1+\cfrac{1}{2+\cfrac{1}{2+\cfrac{1}{2+\cfrac{1}{2+\dots}}}}\]

    \[\frac{\sqrt{\cfrac{5}{2}}+1}{2}=1+\cfrac{1}{3+\cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{1+\cfrac{1}{3+\cfrac{1}{2+\dots}}}}}}=1.290569415042095\dots\]

\displaystyle \frac{\sqrt{3}+1}{2}=1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\dots}}}}}}=1.366025403784439\dots

\displaystyle \frac{\sqrt{\cfrac{7}{2}}+1}{2}=1+\cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{3+\dots}}}}}}=1.435414346693486\dots

\displaystyle \frac{\sqrt{10}+2}{3}=1+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\dots}}}}}}=1.720759220056127\dots

non-repeating:

\displaystyle \text{1/Continued Fraction Constant}=1+\cfrac{1}{2+\cfrac{1}{3+\cfrac{1}{4+\cfrac{1}{5+\dots}}}}
=1.4331274267\dots

    \[\pi=3+\cfrac{1}{7+\cfrac{1}{15+\cfrac{1}{1+\cfrac{1}{292+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{3+\dots}}}}}}}}}}\]

    \[e=2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{4+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{6+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{8+\dots}}}}}}}}}}}\]

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