Tagged Questions
1
vote
1answer
93 views
Continued fractions with $n$ layers
Solve the equation
$$x=2+\dfrac1{2+\dfrac1{...2+\dfrac1{2+\dfrac1x}}}$$
Where there are n layers in the fraction
15
votes
1answer
560 views
What was Ramanujan's solution?
The wikipedia entry on Ramanujan contains the following passage:
One of his remarkable capabilities was the rapid solution for
problems. He was sharing a room with P. C. Mahalanobis who had a
...
6
votes
4answers
321 views
How to detect when continued fractions period terminates
I'm doing continued fractions arithmetic. Is there a method to detect when a continued fractions period terminates?
Let me give you an example:
$\sqrt{2} = [1; \overline{2}]$, $\sqrt{7} = [2; ...
1
vote
1answer
1k views
Converting a square root into a simple continued fraction
One can convert a square root $\sqrt{n}$ into a continued fraction $[a_0; \overline{a_1, a_2, \dots , a_k}]$ following the algebraic algorithm explained here: ...
1
vote
3answers
149 views
Continued fraction form for rational numbers less than $1$
How could we convert a rational number (less than $1$) to the continued fraction form?
This is probably an extension of this question. After reading Bill Dubuque's answer here and here, I got ...
