Next | Continued Fraction Arithmetic | 16 |

The typography is a bit overwhelming

We write: π = [3; 7, 15, 1, 292, 1, ...]

In general, we have

*a*= [*a*_{0};*a*_{1},*a*_{2}, ...]*a*_{0}is the integer part of*a*; α is the fractional part*a*-*a*_{0}*a*_{1},*a*_{2}, ... is the continued fraction expansion of 1/(*a*-*a*_{0})So [

*a*_{0};*a*_{1},*a*_{2}, ...] =*a*_{0}+ 1/[*a*_{1};*a*_{2}, ...]

*a*_{0}can be any integerBut for

*i*≥ 1,*a*_{i}is necessarily*positive*With this restriction, the continued fraction representation is unique (almost)

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