Why is the reciprocal of the fractional part (vs the integer part) taken at each step? Perhaps this is obvious, if so I don't see it. Appreciate your guidance.
Example from Wiki showing reciprocal taken at each step:
Why is the reciprocal of the fractional part (vs the integer part) taken at each step? Perhaps this is obvious, if so I don't see it. Appreciate your guidance.
Example from Wiki showing reciprocal taken at each step:
It's just the Euclidean algorithm.
$$\cfrac{649}{200}=3+\cfrac{49}{200}=3+\cfrac{1}{\cfrac{200}{49}}=3+\cfrac{1}{4+\cfrac{4}{49}}=3+\cfrac{1}{4+\cfrac{1}{\cfrac{49}{4}}}=3+\cfrac{1}{4+\cfrac{1}{12+\cfrac{1}{4}}}$$