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Prof Cohen-
Here is assignment 8. I believe it converts all Roman numerals correctly both ways. I was interested to learn on Wikipedia that Roman numeral only go up to 3999 and don't include 0, which is obvious when you think about it, but I'd never though about it before. The code is kind of bloated; I'm sure there is a more elegant way to do this, but I found this to be a very interesting assignment.
For the Golden Ratio, I found it efficient to just calculate a large fibonacci ratio and then use round to get the desired precision. It seems to work, but I hope I didn't side step the real solution.
Tim