amistre64
  • amistre64
Continued fractions ...
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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amistre64
  • amistre64
a continued fraction can be constructed by taking subsequent recpiricals
amistre64
  • amistre64
\[\frac pq=\frac{1}{q/p}\] i was wondering how they got it for like sqrt(2)
amistre64
  • amistre64
yes, like that

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mathslover
  • mathslover
|dw:1346859847284:dw|
mathslover
  • mathslover
is this a tutorial or a question?
amistre64
  • amistre64
\[\sqrt{2}=1+(\sqrt{2}-1)=1+\cfrac{1}{\frac{1}{\sqrt{2}-1}}\] \[1+\cfrac{1}{\frac{1}{\sqrt{2}-1}*\frac{\sqrt{2}+1}{\sqrt{2}+1}}=1+\cfrac{1}{\frac{\sqrt{2}+1}{2-1}}\] a little of both
amistre64
  • amistre64
i like how the bump timer fakes you out; it shows the button but says you cant when you hit it lol
mathslover
  • mathslover
lol that happens with me sometimes
amistre64
  • amistre64
how do we find the continued fraction of pi?
amistre64
  • amistre64
not that these things are unique, but i still have to wonder
mathslover
  • mathslover
hmn for that you will have to wait just for 1 min.. please
mathslover
  • mathslover
1+pi -1 = pi 1 + 1/(1/pi) -1 = pi correct?
mathslover
  • mathslover
\[\large{1+\pi -1=\pi}\] \[\large{1+\cfrac{1}{\frac{1}{\pi}}-1=\pi}\]
amistre64
  • amistre64
that is correct so far, but im unsure how that helps us proceed
amistre64
  • amistre64
you would most likely want to reciprocate the last 2 terms together
amistre64
  • amistre64
hmm\[4+\pi-4\] \[4+\frac{1}{\pi-4}\] i cant see it from there either
amistre64
  • amistre64
i spose in teh end i could just google it :) but what fun is there in that
amistre64
  • amistre64
\[3+\frac{1}{\pi-3}\] \[3+\frac{1}{.14159...}\frac{10}{10}\] \[3+\frac{10}{1+(1.4159...)-1}\] \[3+\cfrac{10}{1+\cfrac{1}{(1.4159...)-1}}\] \[3+\cfrac{10}{1+\cfrac{1}{(.4159...)}\cfrac{10}{10}}\] \[3+\cfrac{10}{1+\cfrac{10}{4+(4.159...)-4}}\] that seems to be a run on it, but you would have to know the value of pi to begin with id assume
mathslover
  • mathslover
:) that is great work...

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