## amistre64 Group Title Continued fractions ... one year ago one year ago

1. amistre64 Group Title

a continued fraction can be constructed by taking subsequent recpiricals

2. amistre64 Group Title

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

3. amistre64 Group Title

yes, like that

4. mathslover Group Title

|dw:1346859847284:dw|

5. mathslover Group Title

is this a tutorial or a question?

6. amistre64 Group Title

$\sqrt{2}=1+(\sqrt{2}-1)=1+\cfrac{1}{\frac{1}{\sqrt{2}-1}}$ $1+\cfrac{1}{\frac{1}{\sqrt{2}-1}*\frac{\sqrt{2}+1}{\sqrt{2}+1}}=1+\cfrac{1}{\frac{\sqrt{2}+1}{2-1}}$ a little of both

7. amistre64 Group Title

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

8. mathslover Group Title

lol that happens with me sometimes

9. amistre64 Group Title

how do we find the continued fraction of pi?

10. amistre64 Group Title

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

11. mathslover Group Title

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

12. mathslover Group Title

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

13. mathslover Group Title

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

14. amistre64 Group Title

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

15. amistre64 Group Title

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

16. amistre64 Group Title

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

17. amistre64 Group Title

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

18. amistre64 Group Title

$3+\frac{1}{\pi-3}$ $3+\frac{1}{.14159...}\frac{10}{10}$ $3+\frac{10}{1+(1.4159...)-1}$ $3+\cfrac{10}{1+\cfrac{1}{(1.4159...)-1}}$ $3+\cfrac{10}{1+\cfrac{1}{(.4159...)}\cfrac{10}{10}}$ $3+\cfrac{10}{1+\cfrac{10}{4+(4.159...)-4}}$ 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 Group Title

:) that is great work...