One topic which might be interesting here is a continued-fraction library. The golden ratio has a nice representation as the infinite stream [1, 1, 1, 1, ...] b

One topic which might be interesting here is a continued-fraction library. The golden ratio has a nice representation as the infinite stream [1, 1, 1, 1, ...] because it is 1 + 1/(1 + 1/(1 + ...)), a fact which also makes it the most irrational number. If continued-fraction algorithms have developed to the point where you can do arbitrary exponentiations of a continued fraction, then you can just calculate the result to one decimal place and round and you'll get the right result.