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rename statics/euler and sync b93 code with main repo

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Mike Schwörer
2017-11-20 17:38:54 +01:00
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www/statics/euler/Euler_Problem-057_description.md Normal file
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It is possible to show that the square root of two can be expressed as an infinite continued fraction.
~~~
sqrt(2) = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...
~~~
By expanding this for the first four iterations, we get:
~~~
1 + 1/2 = 3 /2 = 1.5
1 + 1/(2 + 1/2) = 7 /5 = 1.4
1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...
1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...
~~~
The next three expansions are `99/70`, `239/169`, and `577/408`, but the eighth expansion, `1393/985`, is the first example where the number of digits in the numerator exceeds the number of digits in the denominator.
In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?