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amistre64

  • 3 years ago

Continued fractions ...

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  1. amistre64
    • 3 years ago
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    a continued fraction can be constructed by taking subsequent recpiricals

  2. amistre64
    • 3 years ago
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    \[\frac pq=\frac{1}{q/p}\] i was wondering how they got it for like sqrt(2)

  3. amistre64
    • 3 years ago
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    yes, like that

  4. mathslover
    • 3 years ago
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    |dw:1346859847284:dw|

  5. mathslover
    • 3 years ago
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    is this a tutorial or a question?

  6. amistre64
    • 3 years ago
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    \[\sqrt{2}=1+(\sqrt{2}-1)=1+\cfrac{1}{\frac{1}{\sqrt{2}-1}}\] \[1+\cfrac{1}{\frac{1}{\sqrt{2}-1}*\frac{\sqrt{2}+1}{\sqrt{2}+1}}=1+\cfrac{1}{\frac{\sqrt{2}+1}{2-1}}\] a little of both

  7. amistre64
    • 3 years ago
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    i like how the bump timer fakes you out; it shows the button but says you cant when you hit it lol

  8. mathslover
    • 3 years ago
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    lol that happens with me sometimes

  9. amistre64
    • 3 years ago
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    how do we find the continued fraction of pi?

  10. amistre64
    • 3 years ago
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    not that these things are unique, but i still have to wonder

  11. mathslover
    • 3 years ago
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    hmn for that you will have to wait just for 1 min.. please

  12. mathslover
    • 3 years ago
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    1+pi -1 = pi 1 + 1/(1/pi) -1 = pi correct?

  13. mathslover
    • 3 years ago
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    \[\large{1+\pi -1=\pi}\] \[\large{1+\cfrac{1}{\frac{1}{\pi}}-1=\pi}\]

  14. amistre64
    • 3 years ago
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    that is correct so far, but im unsure how that helps us proceed

  15. amistre64
    • 3 years ago
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    you would most likely want to reciprocate the last 2 terms together

  16. amistre64
    • 3 years ago
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    hmm\[4+\pi-4\] \[4+\frac{1}{\pi-4}\] i cant see it from there either

  17. amistre64
    • 3 years ago
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    i spose in teh end i could just google it :) but what fun is there in that

  18. amistre64
    • 3 years ago
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    \[3+\frac{1}{\pi-3}\] \[3+\frac{1}{.14159...}\frac{10}{10}\] \[3+\frac{10}{1+(1.4159...)-1}\] \[3+\cfrac{10}{1+\cfrac{1}{(1.4159...)-1}}\] \[3+\cfrac{10}{1+\cfrac{1}{(.4159...)}\cfrac{10}{10}}\] \[3+\cfrac{10}{1+\cfrac{10}{4+(4.159...)-4}}\] that seems to be a run on it, but you would have to know the value of pi to begin with id assume

  19. mathslover
    • 3 years ago
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    :) that is great work...

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