Golden iteration
The expression converges to the golden ratio φ. Another way to say this is that the sequence defined by x0 = 1 and for n > 0 converges to φ. This post will be about how it converges. I wrote a little script to look at the error in approximating φ by xn and noticed that the error is about three times smaller at each step. Here’s why that observation was correct. The ratio of the error at […]