It's easy to obtain four equal parts from a rectangle with three cuts: just make four strips. It's also easy to obtain four equal parts from a rectangle with two cuts: make a horizontal and a vertical cut. Is it possible to take a sheet of paper (not necessarily rectangular) and cut it in four equal parts with just a cut? The sheet cannot be folded, and the cut must be a continuous line.
Roll the paper into a cylinder such that the two edges that go down the inside and the outside are aligned and that there are 4 complete turns in the cylinder. Cut down the point where the edges align.
That's true provided you have an ideal sheet of paper (area but no thickness). Real-world paper having thickness means the inner turn would be slightly shorter than the next one out... and so on to the outside. With a paper thickness of t the difference in width from the outside to the inside piece would be 6t. In the real world, you could buckle the paper while rolling it such that the inside turn had 6t more than 1 rotation in it.
This would work for more or less than 4 as well, though there would be an upper bound where you couldn't roll the paper and accommodate the extra length for the innermost turn.
Well, if the paper doesn't have to be rectangular, you can cut an equilateral triangle into four smaller ones. Go from the midpoint of each side to the next. That's a continuous line, although it turns 120 degrees.