I recently found an continued fraction representation of $\pi$, and I wondered how can I make an continued fraction that converges into a number?
The MAIN question is: how do you make a continued fraction for any number and can every number be represented as continued fraction?
Some SPECIFIC questions:
- How is an continued fraction for any number x generated? Is there an algorithm and what is it?
- Give an example of the algorithm on some irrational number like $\sqrt[3]{15}$ and on some rational number like $0.8713241$.
- Can every number be represented as a continued fraction?
- Do continued fractions for complex numbers exist?
Don't vote down for no reason. I just learned about continued fractions and I don't really know anything about them.