PFG = Paper Folding Golf
You bought a piece of paper from your local op shop, but your shop is always dodgy. So instead of a normal piece of A4, you got an infinitely long strip, a metre wide.
(Actually, it's a bit strange, it seems to have a flaw that causes it to change size to a yard wide when you cross the border into the US. You live near the border in Canada)
Anyway, you want to fold it some number of times then make a single straight cut across the paper you get a rectangle (you still need to find a way to make the line exactly perpendicular to the edge of the paper).
This rectangle should have the property that if you cut its width from its length, you will get another rectangle that has the same ratio of length to width, which will mean you can get a pretty spiral of squares and nice-looking rectangles.
- No tools apart from the paper, folding (is that a tool?) and the magical one-shot straight-line cutter allowed.
- Your paper is really semi-infinite, it has one finite edge.
- Because of magic, your paper doesn't form a black hole under its gravity or anything. It somehow tapers at the end into an infinitely dense roll with weight 50 grams and of diameter 5cm (2" in the US) which you can unroll and re-roll at will without changing its properties. Outside of the roll the paper acts like normal paper.
Quick check of possible minimality:
I got $min(folds)\le4$.
Note (may help?):
It is said that this rectangle looks the nicest.
Googling is prohibited! D: Hence the no-computers tag!