## amistre64 3 years ago Continued fractions ...

1. amistre64

a continued fraction can be constructed by taking subsequent recpiricals

2. amistre64

$\frac pq=\frac{1}{q/p}$ i was wondering how they got it for like sqrt(2)

3. amistre64

yes, like that

4. mathslover

|dw:1346859847284:dw|

5. mathslover

is this a tutorial or a question?

6. 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

7. amistre64

i like how the bump timer fakes you out; it shows the button but says you cant when you hit it lol

8. mathslover

lol that happens with me sometimes

9. amistre64

how do we find the continued fraction of pi?

10. amistre64

not that these things are unique, but i still have to wonder

11. mathslover

hmn for that you will have to wait just for 1 min.. please

12. mathslover

1+pi -1 = pi 1 + 1/(1/pi) -1 = pi correct?

13. mathslover

$\large{1+\pi -1=\pi}$ $\large{1+\cfrac{1}{\frac{1}{\pi}}-1=\pi}$

14. amistre64

that is correct so far, but im unsure how that helps us proceed

15. amistre64

you would most likely want to reciprocate the last 2 terms together

16. amistre64

hmm$4+\pi-4$ $4+\frac{1}{\pi-4}$ i cant see it from there either

17. amistre64

i spose in teh end i could just google it :) but what fun is there in that

18. 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

19. mathslover

:) that is great work...