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Calculate the quadratic irrational number $\alpha$ given by the periodic continued fraction $\alpha = \overline{ [1,2,1] } $.

To be honest I am not sure how to tackle this one. I know the algorithm to construct a continued fraction given $\alpha$, but I am unsure how to reverse this algorithm.

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1 Answer 1

up vote 3 down vote accepted

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

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I feel embarassed,( I am still learning cont. fractions, so sorry for my ignorant question). Thanks for your quick reply! – ClausW Feb 25 '12 at 12:26

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