Hello everyone!

I was playing around with continued fractions last week, and I stumbled across a nice pattern that I hadn't seen before.  I thought it might be interesting to talk about it here.

Let's start with a motivating question.  Consider the number below:

,

extending on infinitely.  It's possible to prove that continued fractions always converge (that is, they come out to actual numbers), so is well-defined.  So what's its value?

Continue reading Continued Fractions, the Golden Ratio, and Fibonacci →

by