Yet another Fibonacci mini-challenge (HP-42S/Free42)

[pier4r]

(12-07-2018 03:41 PM)Gerson W. Barbosa Wrote:  While testing it, I noticed that \(\varphi^{39}\approx \frac{\pi ^{17}}{2}\). A little tweaking, making use of the apparent \(\sqrt{2}\) factors present in both sides of the expression, gives

How? I mean it is not that one computes pi to the 17 every other day. I am really interested how it comes to your mind to compute such values.

Or you go through all the initial exponents. Say, 1 to 30 ?