Next | Continued Fraction Arithmetic | 24 |

But in 1972, Bill Gosper solved the problem of general arithmetic on continued fractions

Suppose

*x*is a continued fraction, possibly infiniteThink of it as an object (in the sense of "object-oriented programming")

There is a method we can use to ask it for its next term

When we do this, it will also modify its internal state

Next time we ask for the next term, we get the

*next*next term

Terms might be stored internally, or might be computed only on demand

If we only need a certain amount of precision, we can stop reading after a while

The work to calculate the remaining terms will not be done until we need it

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