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A Python file to play with a special continued fraction. If you don't have a Python interpreter, try running it in an online one (copy and paste the code), like: http://repl.it/ http://codepad.org/ http://labs.codecademy.com/
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| def x(k): | |
| """Numerically investigate the continued fraction x = | |
| 1 + 1 | |
| ________________ | |
| 1 + 1 | |
| __________ | |
| 1 + 1 | |
| _____ | |
| ... | |
| We won't be able to go out to infinity, so we'll use a counter to take only | |
| a (large) finite number of steps down this fraction. | |
| This is a recursive function, in that it will call itself until a certain | |
| stopping criterion is met. If our counter k is less than 1, we'll return | |
| 1; this is the stopping criterion---or base case---of our recursion. If | |
| not, we'll return 1 + 1 / x(k - 1) (our recursive step). | |
| """ | |
| if k <= 1: | |
| return 1.0 | |
| else: | |
| return 1.0 + 1.0 / x(k - 1) | |
| # Now we'll see this in action | |
| if __name__ == '__main__': | |
| # Print out 250 steps of our continued fraction | |
| print(x(250)) # Does the output look familiar? |
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