Continued fraction: Difference between revisions
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The ''continued-fraction'' function thus returns a lazy list of functions where the variable plays the role of the «<math>\ddots</math>» symbol in the usual representation. The main advantage is that the definition of the function does not need to know for which rank n it is computed. This is arguably closer to the mathematical definition. |
The ''continued-fraction'' function thus returns a lazy list of functions where the variable plays the role of the «<math>\ddots</math>» symbol in the usual representation. The main advantage is that the definition of the function does not need to know for which rank n it is computed. This is arguably closer to the mathematical definition. |
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'''Extra credit''': |
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The value of <math>\pi/2</math> can be related to a pseudo-continued fraction of the harmonic sequence: |
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:<math>\pi/2 = 1 + \cfrac{1}{1 + \cfrac{1}{1/2 + \cfrac{1}{1/3+ \ddots}}}</math> |
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With the same code as above, this could be written: |
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<lang Perl 6>printf "π/2 ≈ %.9f\n", continued-fraction((1 X/ 1, 1 .. *), (1 xx *))[1000](Inf);</lang> |
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=={{header|PL/I}}== |
=={{header|PL/I}}== |
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